Conclusions - 製程能力指標Yq/Y複式抽樣之信賴下限

In this thesis, we introduce a new process capability index Y Y

/ . The index

/

Y Y indicates how close a conformed product comes to meeting 100% customer satisfaction. For customers, it may be a more direct and precise index to measure how well a process can meet their requirements.

The index Y Y

/ has some similar properties to quality yield, such as it does not rely on the normality assumption; It goes from zero to one and compares the quality of different characteristics of a product on a single percentage scale.

Although new capability indices have been developed for non-normal distributions, those indice s are harder to compute and interpret, and are sensitive to data peculiarities. If a process is clearly non-normal, there is some questions as to whether any process index is valid or should even be calculated. In this thesis, the nonparametric is computationally intensive but an effective estimation bootstrap method is applied to the Y Y

/ estimator ˆ Y to obtain the lower confidence

bounds. This approach makes it feasible for the engineers to perform approximate process quality testing using the calculated Y Y

/ .

Based on the simulations we conducted, the best of the four bootstrap methods is BCPB, which consistently has a smallest lower confidence bound so that it has the highest proportion of coverage and provides the most conservative bound for capability testing. The difference is the largest for small sample sizes and diminishing substantially as n increase. For all four of the bootstrap methods, the tendency to increase to the expected values of 0.95 and 0.975 are fast as n is small to slow as n goes larger. Therefore, we recommend that one calculate a lower confidence limit on Y Y

/ using the BCPB method and reinforces the need for

“large samples” to estimate the index Y Y

/ by bootstrap methods.

References

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_pm

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_pk

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_pm

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^rd

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indices. Journal of Quality Technology, 24(4), 188-195.

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_pm

with application to production yield assurance.

International Journal of Production Research, 41(15), 3581-3599.

Appendix A.

Table 16.1. Normal process with  ,T 0.958, 0.671 and 0.3.



Y_q/Y



Y_q Y

T

0.90 0.958 0.898 0.998

T

^0.95 ^0.671 ^0.94999 ^0.99999

T

^0.99 ^0.300 ^0.990 ^1.000

Table 16.2. Normal process with  T ( /8)d , 1.163, 0.88 and 0.556

.



Y_q/Y



Y_q Y

0 T( /8)d 0.85 1.163 0.838 0.986

0 T( /8)d 0.90 0.880 0.899 0.999

0 T( /8)d 0.95 0.556 0.94999 0.99999

Table 16.3. Normal process with  T ( / 4)d , 1.322, 0.928 and 0.581.



Y_q/Y



Y_q Y

0 T( /4)d 0.80 1.322 0.763 0.953

0 T( /4)d 0.85 0.928 0.843 0.992

0 T( /4)d 0.90 0.581 0.89995 0.99995

Table 17.1. Student’s t process with k 3 and  .T

USL LSL Yq /Y Y_q Y

3.936 -3.936 0.90 0.874 0.971

6.363 - 6.363 0.95 0.943 0.992

16.105 -16.105 0.99 0.989 0.999

Table 17.2. Student’s t process with k 3 and  T 0.5.

USL LSL Y_q /Y Yq Y

4.808 -3.808 0.90 0.878 0.976

7.309 -6.309 0.95 0.944 0.993

17.417 -16.417 0.99 0.98955 0.99955

Table 17.3. Student’s t process with k 3 and   .T 1

USL LSL Y_q /Y Yq Y

4.808 -4.233 0.90 0.885 0.984

8.960 -6.960 0.95 0.946 0.995

20.115 -18.115 0.99 0.98969 0.99968

Table 17.4. Student’s t process with k 10 and  .T

USL LSL Y_q /Y Y_q Y

3.380 -3.380 0.90 0.893 0.993

4.964 -4.964 0.95 0.949 0.999

11.180 -11.180 0.99 0.98999 0.99999

Table 17.5. Student’s t process with k 10 and  T 0.5.

USL LSL Yq /Y Y_q Y

4.248 -3.248 0.90 0.898 0.998

5.953 -4.953 0.95 0.94990 0.99989

12.747 -11.747 0.99 0.98999 0.99999

Table 17.6. Student’s t process with k 10 and   .T 1

USL LSL Y_q /Y Yq Y

5.680 -3.680 0.90 0.898 0.998

7.699 -5.699 0.95 0.94990 0.99989

16.000 -14.000 0.99 0.98999 0.99999

Table 17.7. Student’s t process with k 20 and  .T

USL LSL Y_q /Y Yq Y

3.257 -3.257 0.90 0.896 0.996

4.707 -4.707 0.95 0.94987 0.99986

10.541 -10.541 0.99 0.98999 0.99999

Table 17.8. Student’s t process with k 20 and  T 0.5.

USL LSL Y_q /Y Y_q Y

4.128 -3.128 0.90 0.897 0.997

5.713 -4.713 0.95 0.94993 0.99992

12.167 -11.167 0.99 0.98999 0.99999

Table 17.9. Student’s t process with k 20 and   .T 1

USL LSL Yq /Y Y_q Y

5.570 -3.570 0.90 0.899 0.999

7.500 -5.500 0.95 0.94999 0.99999

15.530 -13.530 0.99 0.98999 0.99999

Table 18.1. Chi-squared process with k 12 and  .T

USL LSL Y_q /Y Yq Y

19.278 4.722 0.75 0.663 0.885

21.150 2.850 0.80 0.759 0.948

23.256 0.744 0.85 0.828 0.974

Table 18.2. Chi-squared process with k 12 and  T 0.5.

USL LSL Y_q /Y Yq Y

20.212 4.788 0.75 0.676 0.901

22.075 2.925 0.80 0.767 0.959

24.129 0.871 0.85 0.833 0.980

Table 18.3. Chi-squared process with k 12 and   .T 1

USL LSL Y_q /Y Y_q Y

21.206 4.794 0.75 0.688 0.917

23.061 2.939 0.80 0.775 0.969

25.090 0.910 0.85 0.838 0.986

Table 18.4. Chi-squared process with k 12 and  T 0.5.

USL LSL Yq /Y Y_q Y

18.405 4.595 0.75 0.650 0.866

20.293 2.707 0.80 0.748 0.936

22.486 0.514 0.85 0.822 0.968

Table 18.5. Chi-squared process with k 12 and   .T 1

USL LSL Y_q /Y Yq Y

17.593 4.407 0.75 0.635 0.846

19.511 2.489 0.80 0.737 0.921

21.844 0.156 0.85 0.817 0.961

Table 18.6. Chi-squared process with k 15 and  .T

USL LSL Y_q /Y Yq Y

23.111 6.889 0.75 0.659 0.879

25.318 4.682 0.80 0.759 0.949

27.749 2.251 0.85 0.830 0.977

Table 18.7. Chi-squared process with k 15 and  T 0.5.

USL LSL Y_q /Y Y_q Y

24.005 6.995 0.75 0.670 0.893

26.207 4.793 0.80 0.766 0.958

28.589 2.411 0.85 0.834 0.982

Table 18.8. Chi-squared process with k 15 and   .T 1

USL LSL Yq /Y Y_q Y

24.958 7.042 0.75 0.679 0.906

27.157 4.843 0.80 0.773 0.966

29.512 2.488 0.85 0.838 0.986

Table 18.9. Chi-squared process with k 15 and  T 0.5.

USL LSL Y_q /Y Y_q Y

22.273 6.727 0.75 0.648 0.864

24.494 4.506 0.80 0.751 0.938

27.005 1.995 0.85 0.826 0.971

Table 18.10. Chi-squared process with k 15 and   .T 1

USL LSL Yq /Y Y_q Y

21.492 6.508 0.75 0.636 0.848

23.741 4.259 0.80 0.742 0.927

26.373 1.627 0.85 0.821 0.966

Table 18.11. Chi-squared process with k 20 and  .T

USL LSL Y_q /Y Yq Y

29.328 10.672 0.75 0.655 0.873

32.007 7.993 0.80 0.759 0.949

34.917 5.083 0.85 0.831 0.979

Table 18.12. Chi-squared process with k 20 and  T 0.5.

USL LSL Y_q /Y Yq Y

30.175 10.825 0.75 0.663 0.884

32.852 8.148 0.80 0.765 0.956

35.717 5.283 0.85 0.836 0.983

Table 18.13. Chi-squared process with k 20 and   .T 1

USL LSL Y_q /Y Y_q Y

31.076 10.924 0.75 0.670 0.894

33.756 8.244 0.80 0.770 0.962

36.593 5.407 0.85 0.838 0.986

Table 18.14. Chi-squared process with k 20 and  T 0.5.

USL LSL Yq /Y Y_q Y

28.532 10.468 0.75 0.646 0.861

31.223 7.777 0.80 0.753 0.941

34.203 4.797 0.85 0.829 0.975

Table 18.15. Chi-squared process with k 20 and   .T 1

USL LSL Y_q /Y Yq Y

27.788 10.212 0.75 0.637 0.850

30.505 7.495 0.80 0746 0.933

33.586 4.414 0.85 0.825 0.971

Table 19.1. Gamma process with 12, 2, and  .T

USL LSL Y_q /Y Yq Y

9.300 2.700 0.75 0.759 0.949

10.112 1.888 0.80 0.833 0.980

11.292 0.708 0.85 0.895 0.994

Table 19.2. Gamma process with 12, 2, and  T 0.5.

USL LSL Y_q /Y Y_q Y

10.201 2.799 0.80 0.776 0.970

10.992 2.008 0.85 0.843 0.991

12.125 0.875 0.90 0.898 0.998

Table 19.3. Gamma process with 12, 2, and   .T 1

USL LSL Yq /Y Y_q Y

11.301 2.699 0.80 0.788 0.985

12.109 1.891 0.85 0.848 0.997

13.304 0.696 0.90 0.89951 0.99946

Table 19.4. Gamma process with 12, 2, and  T 0.5.

USL LSL Y_q /Y Y_q Y

8.637 2.363 0.80 0.737 0.921

9.559 1.441 0.85 0.822 0.967

10.920 0.803 0.90 0.893 0.992

Table 19.5. Gamma process with 12, 2, and   .T 1

USL LSL Yq /Y Y_q Y

7.374 2.626 0.75 0.593 0.790

8.325 1.675 0.80 0.722 0.902

9.496 0.504 0.85 0.820 0.965

Table 19.6. Gamma process with 15, 2, and  .T

USL LSL Y_q /Y Yq Y

11.203 3.797 0.80 0.759 0.948

12.128 2.872 0.85 0.834 0.981

13.444 1.556 0.90 0.896 0.995

Table 19.7. Gamma process with 15, 2, and  T 0.5.

USL LSL Y_q /Y Yq Y

12.069 3.931 0.80 0.773 0.966

12.974 3.026 0.85 0.842 0.990

14.244 1.756 0.90 0.898 0.998

Table 19.8. Gamma process with 15, 2, and   .T 1

USL LSL Y_q /Y Y_q Y

13.128 3.872 0.80 0.784 0.980

14.048 2.952 0.85 0.847 0.996

15.367 1.633 0.90 0.899 0.999

Table 19.9. Gamma process with 15, 2, and  T 0.5.

USL LSL Yq /Y Y_q Y

10.556 3.444 0.80 0.741 0.927

11.577 2.423 0.85 0.825 0.971

13.055 0.995 0.90 0.894 0.993

Table 19.10. Gamma process with 15, 2, and   .T 1

USL LSL Y_q /Y Yq Y

9.183 3.817 0.75 0.602 0.803

10.207 2.793 0.80 0.728 0.909

11.440 1.560 0.85 0.822 0.967

Table 19.11. Gamma process with 20, 2, and  .T

USL LSL Y_q /Y Yq Y

14.290 5.710 0.80 0.759 0.948

15.379 4.621 0.85 0.835 0.983

16.897 3.103 0.90 0.896 0.996

Table 19.12. Gamma process with 20, 2, and  T 0.5.

USL LSL Y_q /Y Y_q Y

15.113 5.887 0.80 0.770 0.962

16.185 4.815 0.85 0.841 0.990

17.659 3.341 0.90 0.898 0.998

Table 19.13. Gamma process with 20, 2, and   .T 1

USL LSL Yq /Y Y_q Y

16.118 5.882 0.80 0.779 0.974

17.203 4.797 0.85 0.846 0.995

18.714 3.286 0.90 0.899 0.999

Table 19.14. Gamma process with 20, 2, and  T 0.5.

USL LSL Y_q /Y Y_q Y

13.663 5.337 0.80 0.746 0.932

14.832 4.168 0.85 0.828 0.975

16.490 2.510 0.90 0.895 0.994

Table 19.15. Gamma process with 20, 2, and   .T 1

USL LSL Yq /Y Y_q Y

12.133 5.867 0.75 0.612 0.816

13.288 4.712 0.80 0.734 0.918

14.622 3.378 0.85 0.825 0.970

Table 20.1. Weibull process with 10, 3.6 , and  .T

USL LSL Y_q /Y Yq Y

14.630 3.392 0.80 0.768 0.960

16.012 2.010 0.85 0.844 0.993

17.787 0.235 0.90 0.89969 0.99965

Table 20.2. Weibull process with 10, 3.6 , and   .T 0.5

USL LSL Y_q /Y Yq Y

15.181 3.841 0.80 0.766 0.957

16.617 2.405 0.85 0.843 0.992

18.437 0.585 0.90 0.89986 0.99985

Table 20.3. Weibull process with 10, 3.6 , and   .T 1

USL LSL Y_q /Y Y_q Y

15.905 4.117 0.80 0.764 0.955

17.436 2.586 0.85 0.843 0.992

19.351 0.671 0.90 0.89993 0.99992

Table 20.4. Weibull process with 10, 3.6 , and   .T 0.5

USL LSL Yq /Y Y_q Y

12.881 4.141 0.75 0.657 0.876

14.230 2.792 0.80 0.769 0.962

15.608 1.414 0.85 0.843 0.992

Table 20.5. Weibull process with 10, 3.6 , and   .T 1

USL LSL Y_q /Y Yq Y

12.598 3.424 0.75 0.659 0.879

13.983 2.039 0.80 0.769 0.961

15.409 0.613 0.85 0.843 0.991

Table 20.6. Weibull process with 10, 6, and  .T

USL LSL Y_q /Y Yq Y

12.776 5.779 0.80 0.760 0.951

13.663 4.892 0.85 0.837 0.985

14.887 3.667 0.90 0.898 0.998

Table 20.7. Weibull process with 10, 6 , and   .T 0.5

USL LSL Y_q /Y Y_q Y

13.174 6.38 0.80 0.744 0.929

14.167 5.387 0.85 0.829 0.976

15.546 4.008 0.90 0.896 0.996

Table 20.8. Weibull process with 10, 6 , and   .T 1

USL LSL Yq /Y Y_q Y

13.908 6.647 0.80 0.733 0.917

15.105 5.449 0.85 0.828 0.974

16.663 3.891 0.90 0.897 0.997

Table 20.9. Weibull process with 10, 6 , and   .T 0.5

USL LSL Y_q /Y Y_q Y

12.614 4.941 0.80 0.774 0.968

13.476 4.078 0.85 0.844 0.993

14.658 2.896 0.90 0.8989 0.999

Table 20.10. Weibull process with 10, 6 , and   .T 1

USL LSL Yq /Y Y_q Y

12.659 3.895 0.80 0.784 0.980

13.539 3.015 0.85 0.848 0.997

14.780 1.774 0.90 0.89995 0.99994

Table 20.11. Weibull process with 10, 10 , and  .T

USL LSL Y_q /Y Yq Y

11.664 7.363 0.80 0.756 0.945

12.202 6.825 0.85 0.831 0.978

12.996 6.031 0.90 0.894 0.994

Table 20.12. Weibull process with 10, 10, and  T 0.5.

USL LSL Y_q /Y Yq Y

12.039 7.988 0.80 0.718 0.898

12.738 7.289 0.85 0.815 0.959

13.748 6.279 0.90 0.891 0.990

Table 20.13. Weibull process with 10, 10, and   .T 1

USL LSL Y_q /Y Y_q Y

13.168 7.859 0.80 0.731 0.914

14.059 6.968 0.85 0.827 0.973

15.200 5.827 0.90 0.896 0.995

Table 20.14. Weibull process with 10, 10, and  T 0.5.

USL LSL Yq /Y Y_q Y

11.650 6.377 0.80 0.783 0.979

12.169 5.858 0.85 0.845 0.994

12.937 5.090 0.90 0.899 0.999

Table 20.15. Weibull process with 10, 10, and   .T 1

USL LSL Y_q /Y Yq Y

11.870 5.157 0.80 0.796 0.995

12.430 4.597 0.85 0.850 0.999

13.319 3.708 0.90 0.89996 0.99995

Appendix B.

Table 21A. Average bound and coverage percentage of 95% bootstrap for normal process with T  ,0 USL  ,3 LSL  .3

 

^/2

dUSL LSL

 Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500 T 0.90 SB

PB BCPB

0.876 0.897 0.912 0.915 0.921 0.927 0.933 0.938 0.887 0.907 0.919 0.923 0.926 0.933 0.939 0.943 0.901 0.917 0.928 0.933 0.932 0.940 0.942 0.945 0.861 0.884 0.904 0.907 0.913 0.922 0.926 0.935

0.857 0.869 0.875 0.878 0.882 0.885 0.887 0.890 0.854 0.868 0.873 0.877 0.881 0.884 0.887 0.890 0.850 0.865 0.872 0.876 0.880 0.884 0.887 0.890 0.860 0.871 0.876 0.879 0.882 0.885 0.888 0.890

0.95 SB

PB BCPB

0.863 0.890 0.903 0.907 0.915 0.921 0.928 0.935 0.874 0.903 0.915 0.914 0.923 0.927 0.932 0.938 0.891 0.914 0.927 0.924 0.932 0.934 0.938 0.942 0.846 0.877 0.893 0.896 0.910 0.915 0.921 0.930

0.929 0.934 0.937 0.939 0.941 0.942 0.943 0.945 0.927 0.933 0.936 0.938 0.940 0.942 0.943 0.945 0.925 0.932 0.935 0.938 0.940 0.941 0.943 0.945 0.930 0.935 0.938 0.939 0.941 0.942 0.944 0.945

0.99 SB

PB BCPB

0.851 0.890 0.900 0.904 0.910 0.919 0.925 0.928 0.863 0.899 0.908 0.913 0.916 0.924 0.929 0.930 0.876 0.911 0.915 0.921 0.924 0.931 0.936 0.935 0.840 0.880 0.890 0.894 0.903 0.915 0.918 0.924

0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.989 0.985 0.987 0.987 0.988 0.988 0.988 0.989 0.989 0.985 0.986 0.987 0.988 0.988 0.988 0.989 0.989 0.986 0.987 0.988 0.988 0.988 0.988 0.989 0.989 /8

T d 0.85 SB PB BCPB

0.874 0.906 0.914 0.927 0.929 0.935 0.940 0.945 0.886 0.914 0.922 0.933 0.935 0.938 0.943 0.946 0.899 0.923 0.933 0.939 0.942 0.943 0.946 0.948 0.858 0.896 0.908 0.922 0.923 0.932 0.936 0.941

0.791 0.807 0.815 0.818 0.825 0.828 0.832 0.836 0.787 0.805 0.813 0.817 0.824 0.827 0.832 0.836 0.783 0.802 0.812 0.816 0.823 0.827 0.831 0.835 0.794 0.808 0.816 0.819 0.825 0.828 0.832 0.836

0.90 SB

PB BCPB

0.869 0.895 0.915 0.921 0.923 0.927 0.935 0.936 0.881 0.902 0.925 0.927 0.930 0.932 0.940 0.940 0.895 0.911 0.933 0.933 0.936 0.937 0.946 0.945 0.856 0.884 0.906 0.908 0.919 0.922 0.929 0.931

0.858 0.870 0.874 0.878 0.882 0.884 0.887 0.890 0.855 0.868 0.873 0.877 0.881 0.884 0.887 0.890 0.851 0.866 0.872 0.876 0.880 0.883 0.886 0.890 0.861 0.871 0.876 0.879 0.882 0.885 0.887 0.890

0.95 SB

PB BCPB

0.866 0.889 0.907 0.920 0.919 0.924 0.929 0.931 0.879 0.898 0.913 0.928 0.927 0.931 0.936 0.935 0.895 0.911 0.926 0.936 0.934 0.938 0.941 0.941 0.855 0.878 0.898 0.911 0.911 0.918 0.925 0.929

0.930 0.935 0.938 0.939 0.941 0.943 0.944 0.945 0.928 0.935 0.937 0.939 0.941 0.942 0.944 0.945 0.926 0.933 0.937 0.938 0.940 0.942 0.943 0.945 0.931 0.936 0.938 0.940 0.941 0.943 0.944 0.945 /4

T d 0.80 SB PB BCPB

0.895 0.917 0.923 0.931 0.934 0.939 0.940 0.949 0.908 0.923 0.931 0.937 0.938 0.943 0.943 0.951 0.922 0.934 0.939 0.941 0.943 0.946 0.946 0.953 0.881 0.910 0.917 0.925 0.930 0.935 0.938 0.948

0.727 0.746 0.756 0.762 0.769 0.773 0.778 0.783 0.723 0.744 0.755 0.761 0.768 0.772 0.777 0.782 0.719 0.742 0.753 0.760 0.767 0.772 0.777 0.782 0.730 0.748 0.758 0.763 0.769 0.773 0.778 0.783

0.85 SB

PB BCPB0

0.890 0.912 0.919 0.924 0.930 0.935 0.935 0.941 0.898 0.921 0.925 0.929 0.937 0.938 0.938 0.944 0.909 0.928 0.931 0.939 0.941 0.942 0.941 0.947 0.878 0.903 0.915 0.918 0.927 0.930 0.932 0.938

0.791 0.808 0.816 0.820 0.826 0.829 0.833 0.836 0.788 0.806 0.815 0.819 0.825 0.829 0.832 0.836 0.783 0.804 0.813 0.818 0.825 0.828 0.832 0.836 0.794 0.810 0.817 0.821 0.827 0.830 0.833 0.837

0.90 SB

PB BCPB

0.882 0.906 0.913 0.916 0.928 0.926 0.933 0.941 0.891 0.913 0.916 0.922 0.933 0.932 0.936 0.944 0.903 0.920 0.924 0.929 0.939 0.936 0.940 0.949 0.872 0.897 0.905 0.912 0.923 0.922 0.931 0.938

0.865 0.875 0.880 0.882 0.886 0.887 0.890 0.892 0.864 0.874 0.879 0.882 0.885 0.887 0.890 0.892 0.861 0.873 0.878 0.881 0.885 0.887 0.889 0.892 0.867 0.876 0.880 0.883 0.886 0.888 0.890 0.892 Table 21B. Average bound and coverage percentage of 97.5% bootstrap for normal process with T  ,0 USL  ,3 LSL  .3

T 0.90 SB PB BCPB

0.903 0.926 0.940 0.948 0.953 0.957 0.962 0.968 0.916 0.939 0.948 0.954 0.960 0.963 0.964 0.972 0.928 0.948 0.953 0.959 0.967 0.966 0.968 0.974 0.888 0.911 0.927 0.938 0.945 0.948 0.958 0.965

0.850 0.863 0.870 0.873 0.879 0.881 0.885 0.888 0.845 0.860 0.868 0.872 0.878 0.880 0.884 0.888 0.841 0.858 0.867 0.871 0.877 0.880 0.884 0.888 0.855 0.866 0.872 0.875 0.880 0.882 0.885 0.888

0.95 SB

PB BCPB

0.893 0.919 0.936 0.939 0.946 0.955 0.956 0.965 0.904 0.929 0.947 0.947 0.956 0.959 0.960 0.967 0.918 0.936 0.952 0.953 0.959 0.963 0.964 0.968 0.874 0.907 0.923 0.930 0.939 0.947 0.949 0.961

0.924 0.931 0.934 0.936 0.939 0.940 0.942 0.944 0.922 0.930 0.933 0.936 0.938 0.940 0.942 0.944 0.920 0.928 0.932 0.935 0.938 0.939 0.942 0.943 0.927 0.933 0.935 0.937 0.939 0.941 0.942 0.944

0.99 SB

PB BCPB

0.882 0.922 0.930 0.930 0.943 0.954 0.956 0.960 0.898 0.933 0.942 0.937 0.952 0.960 0.960 0.965 0.909 0.940 0.945 0.943 0.955 0.966 0.962 0.968

0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.984 0.986 0.987 0.987 0.988 0.988 0.988 0.989

Table 21B. (continued)

0.910 0.937 0.945 0.955 0.960 0.959 0.964 0.968 0.921 0.948 0.952 0.963 0.967 0.964 0.966 0.971 0.935 0.954 0.958 0.966 0.971 0.966 0.970 0.974 0.891 0.926 0.936 0.948 0.954 0.954 0.957 0.966

0.779 0.798 0.808 0.812 0.820 0.824 0.829 0.833 0.774 0.796 0.806 0.811 0.819 0.823 0.828 0.833 0.769 0.793 0.804 0.809 0.818 0.823 0.828 0.833 0.785 0.802 0.810 0.814 0.821 0.825 0.829 0.834

0.90 SB

PB BCPB

0.900 0.929 0.939 0.943 0.953 0.957 0.962 0.964 0.912 0.938 0.950 0.953 0.959 0.961 0.969 0.969 0.921 0.948 0.955 0.961 0.964 0.966 0.974 0.971 0.883 0.919 0.928 0.935 0.946 0.952 0.955 0.959

0.849 0.863 0.870 0.874 0.878 0.881 0.885 0.888 0.845 0.860 0.868 0.872 0.877 0.881 0.884 0.888 0.841 0.858 0.866 0.871 0.877 0.880 0.884 0.888 0.854 0.866 0.871 0.875 0.879 0.882 0.885 0.888

0.95 SB

PB BCPB

0.897 0.914 0.936 0.943 0.947 0.953 0.958 0.962 0.906 0.923 0.943 0.950 0.953 0.959 0.963 0.968 0.916 0.931 0.952 0.956 0.957 0.963 0.967 0.970 0.881 0.897 0.924 0.936 0.942 0.947 0.950 0.957

0.926 0.933 0.935 0.937 0.939 0.941 0.943 0.944 0.924 0.931 0.934 0.937 0.939 0.940 0.942 0.944 0.922 0.930 0.934 0.936 0.939 0.940 0.942 0.944 0.928 0.934 0.936 0.938 0.940 0.941 0.943 0.944 /4

T d 0.80 SB PB BCPB

0.925 0.948 0.955 0.958 0.959 0.966 0.970 0.970 0.936 0.957 0.961 0.963 0.964 0.969 0.974 0.972 0.946 0.961 0.966 0.966 0.968 0.970 0.977 0.975 0.910 0.944 0.949 0.950 0.953 0.963 0.966 0.968

0.711 0.735 0.747 0.755 0.762 0.767 0.774 0.780 0.706 0.732 0.745 0.753 0.761 0.766 0.773 0.779 0.701 0.730 0.743 0.752 0.760 0.765 0.773 0.779 0.717 0.738 0.749 0.756 0.763 0.768 0.774 0.780

0.85 SB

PB BCPB0

0.917 0.940 0.953 0.956 0.957 0.965 0.963 0.966 0.928 0.951 0.961 0.962 0.963 0.967 0.965 0.969 0.937 0.958 0.965 0.966 0.966 0.969 0.969 0.970 0.899 0.927 0.943 0.949 0.950 0.962 0.958 0.965

0.782 0.800 0.809 0.814 0.821 0.824 0.829 0.834 0.777 0.797 0.807 0.813 0.820 0.824 0.829 0.834 0.772 0.795 0.805 0.812 0.819 0.823 0.828 0.834 0.788 0.803 0.811 0.816 0.822 0.825 0.830 0.834

0.90 SB

PB BCPB

0.914 0.937 0.947 0.954 0.956 0.962 0.967 0.965 0.925 0.945 0.952 0.959 0.962 0.966 0.970 0.969 0.933 0.950 0.957 0.965 0.965 0.969 0.972 0.970 0.899 0.926 0.941 0.945 0.951 0.958 0.961 0.964

0.860 0.870 0.875 0.879 0.882 0.885 0.888 0.890 0.857 0.869 0.874 0.878 0.882 0.884 0.887 0.890 0.854 0.867 0.873 0.877 0.881 0.884 0.887 0.890 0.863 0.872 0.876 0.880 0.883 0.885 0.888 0.891 Table 22A. Average bound and coverage percentage of 95% bootstrap for Student’s t process with  ,0 k  .3

T Y_c bootstrap

(Coverage percentage ) Samples Size( n) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

0 0.90 SB

PB BCPB

0.836 0.879 0.892 0.912 0.919 0.928 0.933 0.940 0.851 0.888 0.904 0.921 0.925 0.936 0.938 0.943 0.869 0.902 0.919 0.935 0.933 0.945 0.944 0.946 0.820 0.866 0.877 0.901 0.912 0.919 0.928 0.935

0.852 0.864 0.871 0.873 0.879 0.881 0.885 0.888 0.848 0.862 0.869 0.872 0.878 0.880 0.884 0.888 0.842 0.859 0.867 0.871 0.877 0.880 0.884 0.888 0.856 0.866 0.872 0.875 0.880 0.882 0.885 0.888

0.95 SB

PB BCPB

0.773 0.835 0.860 0.877 0.890 0.901 0.914 0.918 0.790 0.849 0.873 0.891 0.902 0.910 0.920 0.924 0.810 0.867 0.884 0.902 0.915 0.924 0.930 0.931 0.754 0.816 0.843 0.863 0.876 0.885 0.904 0.908

0.921 0.928 0.932 0.934 0.937 0.939 0.940 0.943 0.918 0.927 0.930 0.933 0.936 0.938 0.940 0.942 0.914 0.924 0.928 0.931 0.935 0.937 0.939 0.942 0.924 0.930 0.933 0.935 0.937 0.939 0.941 0.943

0.99 SB

PB BCPB

0.670 0.722 0.751 0.769 0.783 0.821 0.830 0.859 0.690 0.739 0.762 0.787 0.796 0.833 0.843 0.869 0.718 0.765 0.788 0.809 0.814 0.854 0.860 0.881 0.645 0.703 0.727 0.745 0.765 0.804 0.811 0.843

0.982 0.984 0.985 0.985 0.986 0.987 0.987 0.988 0.981 0.983 0.984 0.985 0.986 0.986 0.987 0.988 0.980 0.982 0.984 0.984 0.985 0.986 0.986 0.987 0.984 0.985 0.986 0.986 0.987 0.987 0.987 0.988

0.5 0.90 SB

PB BCPB

0.832 0.895 0.903 0.913 0.923 0.923 0.929 0.940 0.846 0.906 0.913 0.921 0.928 0.930 0.934 0.942 0.864 0.917 0.926 0.932 0.936 0.937 0.942 0.947 0.817 0.879 0.889 0.902 0.914 0.918 0.924 0.936

0.854 0.864 0.871 0.875 0.879 0.882 0.885 0.888 0.850 0.862 0.869 0.873 0.878 0.881 0.885 0.888 0.845 0.859 0.867 0.872 0.877 0.880 0.884 0.888 0.858 0.866 0.872 0.876 0.880 0.882 0.885 0.888

0.95 SB

PB BCPB0

0.776 0.834 0.855 0.873 0.895 0.899 0.917 0.927 0.791 0.845 0.869 0.888 0.904 0.906 0.923 0.931 0.811 0.861 0.881 0.903 0.918 0.918 0.933 0.938 0.755 0.813 0.838 0.857 0.880 0.888 0.908 0.918

0.923 0.929 0.932 0.935 0.937 0.939 0.941 0.943 0.920 0.927 0.931 0.934 0.937 0.938 0.940 0.943 0.916 0.924 0.929 0.932 0.936 0.937 0.940 0.942 0.926 0.931 0.934 0.936 0.938 0.939 0.941 0.943

0.99 SB

PB BCPB

0.674 0.736 0.762 0.776 0.793 0.813 0.845 0.873 0.692 0.753 0.779 0.791 0.807 0.830 0.859 0.882 0.721 0.778 0.804 0.810 0.825 0.845 0.872 0.896 0.654 0.717 0.741 0.758 0.777 0.794 0.831 0.862

0.983 0.984 0.985 0.986 0.986 0.987 0.987 0.988 0.982 0.984 0.985 0.985 0.986 0.986 0.987 0.988 0.981 0.983 0.984 0.985 0.985 0.986 0.987 0.987 0.984 0.985 0.986 0.986 0.987 0.987 0.987 0.988

Table 22A. (continued)

1 0.90 SB

PB BCPB

0.845 0.888 0.901 0.909 0.918 0.927 0.932 0.935 0.855 0.897 0.910 0.914 0.927 0.935 0.938 0.938 0.871 0.910 0.923 0.927 0.937 0.944 0.943 0.942 0.828 0.875 0.891 0.896 0.908 0.92 0.929 0.930

0.856 0.868 0.873 0.877 0.881 0.883 0.886 0.889 0.853 0.866 0.872 0.876 0.880 0.883 0.886 0.889 0.848 0.863 0.870 0.874 0.879 0.882 0.885 0.889 0.860 0.870 0.874 0.878 0.882 0.884 0.887 0.890

0.95 SB

PB BCPB

0.784 0.847 0.866 0.871 0.891 0.895 0.904 0.915 0.797 0.857 0.877 0.882 0.903 0.902 0.914 0.919 0.815 0.873 0.893 0.899 0.914 0.912 0.925 0.928 0.765 0.829 0.853 0.863 0.880 0.884 0.895 0.908

0.925 0.930 0.934 0.936 0.938 0.940 0.942 0.944 0.923 0.929 0.933 0.935 0.938 0.939 0.941 0.943 0.919 0.926 0.931 0.934 0.937 0.939 0.941 0.943 0.928 0.932 0.935 0.937 0.939 0.940 0.942 0.944

0.99 SB

PB BCPB

0.694 0.747 0.757 0.793 0.818 0.830 0.841 0.864 0.708 0.764 0.771 0.805 0.833 0.840 0.855 0.872 0.734 0.789 0.792 0.824 0.846 0.857 0.870 0.885 0.672 0.728 0.736 0.775 0.799 0.819 0.824 0.850

0.984 0.985 0.986 0.986 0.987 0.987 0.988 0.988 0.984 0.984 0.986 0.986 0.986 0.987 0.987 0.988 0.983 0.984 0.985 0.985 0.986 0.986 0.987 0.988 0.985 0.986 0.987 0.987 0.987 0.987 0.988 0.988 Table 22B. Average bound and coverage percentage of 97.5% bootstrap for Student’s t process with  ,0 k  .3

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

0 0.90 SB

PB BCPB

0.875 0.913 0.932 0.940 0.951 0.955 0.958 0.963 0.895 0.927 0.942 0.950 0.958 0.962 0.962 0.966 0.904 0.937 0.949 0.957 0.964 0.966 0.968 0.969 0.854 0.894 0.917 0.929 0.943 0.948 0.954 0.957

0.841 0.856 0.864 0.869 0.874 0.877 0.882 0.886 0.835 0.853 0.862 0.867 0.873 0.876 0.881 0.885 0.829 0.849 0.859 0.865 0.872 0.875 0.880 0.885 0.849 0.860 0.867 0.871 0.876 0.878 0.882 0.886

0.95 SB

PB BCPB

0.819 0.867 0.898 0.909 0.915 0.923 0.941 0.955 0.838 0.881 0.913 0.923 0.927 0.932 0.949 0.963 0.854 0.894 0.922 0.932 0.937 0.940 0.955 0.966 0.788 0.847 0.877 0.892 0.899 0.911 0.931 0.946

0.915 0.924 0.928 0.930 0.934 0.936 0.939 0.941 0.911 0.921 0.926 0.929 0.933 0.935 0.938 0.941 0.906 0.918 0.923 0.927 0.932 0.935 0.937 0.940 0.921 0.928 0.930 0.932 0.936 0.937 0.939 0.941

0.99 SB

PB BCPB

0.715 0.774 0.789 0.809 0.841 0.849 0.881 0.884 0.738 0.797 0.810 0.830 0.859 0.870 0.897 0.899 0.762 0.814 0.833 0.849 0.879 0.886 0.907 0.912 0.666 0.739 0.756 0.778 0.814 0.826 0.862 0.866

0.982 0.983 0.984 0.984 0.985 0.986 0.986 0.987 0.981 0.982 0.983 0.984 0.985 0.985 0.986 0.987 0.979 0.981 0.982 0.983 0.984 0.985 0.986 0.987 0.984 0.984 0.985 0.985 0.986 0.986 0.987 0.988

0.5 0.90 SB

PB BCPB

0.875 0.908 0.933 0.942 0.948 0.955 0.959 0.965 0.888 0.921 0.945 0.950 0.956 0.960 0.966 0.970 0.901 0.931 0.953 0.957 0.964 0.963 0.969 0.973 0.852 0.887 0.919 0.930 0.938 0.945 0.952 0.959

0.844 0.859 0.865 0.870 0.875 0.879 0.883 0.886 0.838 0.856 0.862 0.868 0.874 0.878 0.882 0.886 0.833 0.853 0.860 0.866 0.873 0.877 0.881 0.886 0.851 0.863 0.868 0.872 0.876 0.880 0.883 0.887

0.95 SB

PB BCPB0

0.822 0.878 0.891 0.916 0.924 0.933 0.941 0.953 0.842 0.896 0.908 0.930 0.935 0.944 0.947 0.958 0.854 0.910 0.918 0.937 0.942 0.953 0.954 0.962 0.798 0.854 0.870 0.902 0.909 0.918 0.930 0.945

0.917 0.925 0.929 0.931 0.935 0.936 0.939 0.941 0.913 0.922 0.927 0.929 0.934 0.936 0.938 0.941 0.908 0.919 0.925 0.928 0.933 0.935 0.938 0.941 0.922 0.928 0.931 0.933 0.936 0.937 0.940 0.942

0.99 SB

PB BCPB

0.73 0.766 0.803 0.826 0.846 0.862 0.882 0.902 0.753 0.786 0.826 0.841 0.868 0.880 0.897 0.913 0.771 0.810 0.844 0.856 0.881 0.891 0.907 0.921 0.696 0.735 0.776 0.798 0.825 0.837 0.862 0.884

0.981 0.983 0.984 0.985 0.986 0.986 0.987 0.987 0.980 0.983 0.983 0.984 0.985 0.986 0.986 0.987 0.979 0.981 0.982 0.983 0.984 0.985 0.986 0.987 0.983 0.985 0.985 0.986 0.986 0.987 0.987 0.988

1 0.90 SB

PB BCPB

0.885 0.919 0.928 0.943 0.947 0.950 0.959 0.965 0.896 0.930 0.938 0.949 0.952 0.955 0.965 0.969 0.908 0.938 0.948 0.955 0.958 0.963 0.969 0.972 0.865 0.906 0.917 0.934 0.935 0.941 0.951 0.962

0.848 0.862 0.868 0.872 0.877 0.880 0.884 0.887 0.843 0.859 0.866 0.870 0.876 0.879 0.883 0.887 0.838 0.856 0.864 0.868 0.875 0.878 0.883 0.887 0.854 0.865 0.87 0.873 0.878 0.881 0.884 0.888

0.95 SB

PB BCPB0

0.827 0.869 0.889 0.909 0.927 0.932 0.945 0.950 0.844 0.884 0.902 0.921 0.937 0.940 0.954 0.959 0.859 0.895 0.914 0.932 0.942 0.947 0.960 0.965 0.798 0.852 0.872 0.894 0.911 0.919 0.936 0.942

0.919 0.928 0.931 0.933 0.936 0.938 0.940 0.942 0.916 0.925 0.929 0.932 0.935 0.937 0.939 0.942 0.912 0.923 0.927 0.930 0.934 0.936 0.939 0.942 0.924 0.931 0.933 0.935 0.937 0.939 0.941 0.943

0.99 SB

PB BCPB

0.728 0.786 0.816 0.820 0.846 0.858 0.875 0.891 0.754 0.809 0.836 0.844 0.862 0.873 0.894 0.905 0.773 0.828 0.85 0.859 0.879 0.885 0.906 0.913 0.692 0.761 0.787 0.799 0.823 0.841 0.859 0.874

0.983 0.984 0.985 0.985 0.986 0.987 0.987 0.988 0.983 0.983 0.985 0.985 0.986 0.986 0.987 0.988 0.981 0.982 0.984 0.984 0.985 0.986 0.986 0.987 0.985 0.985 0.986 0.986 0.987 0.987 0.988 0.988

Table 23A. Average bound and coverage percentage of 95% bootstrap for Student’s t process with  ,0 k  .10

T Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

0 0.90 SB

PB BCPB

0.854 0.880 0.904 0.908 0.913 0.924 0.930 0.936 0.864 0.888 0.913 0.914 0.921 0.931 0.933 0.938 0.884 0.903 0.924 0.925 0.930 0.937 0.939 0.943 0.838 0.868 0.892 0.898 0.907 0.917 0.924 0.934

0.855 0.868 0.873 0.877 0.881 0.883 0.886 0.889 0.852 0.866 0.872 0.876 0.880 0.882 0.886 0.889 0.848 0.864 0.870 0.874 0.879 0.882 0.885 0.889 0.859 0.870 0.874 0.878 0.882 0.883 0.886 0.890

0.95 SB

PB BCPB

0.837 0.867 0.884 0.895 0.901 0.906 0.919 0.924 0.850 0.877 0.896 0.905 0.910 0.913 0.927 0.931 0.868 0.891 0.909 0.914 0.917 0.921 0.935 0.941 0.823 0.851 0.873 0.884 0.892 0.897 0.913 0.919

0.925 0.932 0.935 0.937 0.939 0.941 0.942 0.944 0.924 0.931 0.934 0.936 0.939 0.940 0.942 0.944 0.921 0.929 0.933 0.935 0.938 0.940 0.942 0.944 0.928 0.934 0.936 0.938 0.94 0.941 0.943 0.944

0.99 SB

PB BCPB

0.829 0.858 0.872 0.884 0.893 0.902 0.913 0.918 0.843 0.870 0.883 0.893 0.903 0.909 0.918 0.925 0.863 0.886 0.901 0.908 0.910 0.917 0.929 0.930 0.808 0.844 0.861 0.871 0.883 0.892 0.905 0.913

0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.984 0.986 0.986 0.987 0.987 0.988 0.988 0.989 0.986 0.987 0.987 0.987 0.988 0.988 0.988 0.989

0.5 0.90 SB

PB BCPB

0.846 0.895 0.906 0.923 0.922 0.920 0.929 0.935 0.860 0.904 0.914 0.931 0.930 0.928 0.934 0.937 0.877 0.917 0.921 0.937 0.941 0.936 0.939 0.942 0.832 0.882 0.894 0.914 0.913 0.916 0.923 0.930

0.857 0.868 0.874 0.876 0.881 0.884 0.887 0.890 0.854 0.866 0.873 0.875 0.880 0.883 0.886 0.889 0.850 0.864 0.871 0.874 0.880 0.882 0.886 0.889 0.860 0.870 0.875 0.877 0.882 0.884 0.887 0.890

0.95 SB

PB BCPB0

0.832 0.869 0.891 0.896 0.901 0.919 0.922 0.927 0.846 0.881 0.898 0.906 0.912 0.927 0.926 0.931 0.863 0.894 0.913 0.916 0.921 0.932 0.934 0.939 0.816 0.855 0.881 0.887 0.890 0.909 0.916 0.923

0.927 0.933 0.936 0.938 0.94 0.941 0.943 0.944 0.925 0.932 0.935 0.937 0.94 0.941 0.942 0.944 0.922 0.93 0.934 0.936 0.939 0.94 0.942 0.944 0.929 0.934 0.937 0.939 0.941 0.942 0.943 0.944

0.99 SB

PB BCPB

0.821 0.864 0.889 0.889 0.897 0.914 0.921 0.930 0.832 0.874 0.901 0.898 0.906 0.921 0.926 0.933 0.850 0.887 0.915 0.908 0.914 0.928 0.933 0.940 0.804 0.847 0.873 0.876 0.887 0.906 0.914 0.923

0.985 0.987 0.987 0.987 0.988 0.988 0.989 0.989 0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.989

1 0.90 SB

PB BCPB

0.855 0.893 0.900 0.919 0.925 0.928 0.931 0.942 0.868 0.902 0.907 0.925 0.931 0.933 0.937 0.946 0.883 0.912 0.917 0.935 0.940 0.937 0.943 0.952 0.841 0.883 0.891 0.911 0.918 0.921 0.926 0.938

0.861 0.871 0.876 0.879 0.883 0.885 0.888 0.890 0.858 0.870 0.875 0.878 0.882 0.885 0.887 0.890 0.855 0.867 0.874 0.877 0.881 0.884 0.887 0.890 0.864 0.873 0.877 0.88 0.883 0.885 0.888 0.891

0.95 SB

PB BCPB0

0.850 0.880 0.892 0.903 0.913 0.926 0.930 0.931 0.863 0.890 0.899 0.911 0.922 0.934 0.936 0.937 0.881 0.900 0.911 0.919 0.931 0.939 0.941 0.941 0.837 0.869 0.879 0.894 0.905 0.917 0.925 0.928

0.929 0.935 0.938 0.939 0.941 0.942 0.943 0.945 0.928 0.934 0.937 0.938 0.941 0.942 0.943 0.945 0.926 0.933 0.936 0.938 0.94 0.942 0.943 0.945 0.931 0.936 0.939 0.939 0.941 0.943 0.944 0.945

0.99 SB

PB BCPB

0.847 0.874 0.895 0.898 0.909 0.912 0.932 0.931 0.862 0.884 0.904 0.904 0.914 0.920 0.938 0.935 0.876 0.899 0.915 0.912 0.919 0.926 0.944 0.939 0.833 0.864 0.885 0.889 0.903 0.903 0.922 0.926

0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.989 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.989 0.985 0.987 0.987 0.988 0.988 0.988 0.989 0.989 0.986 0.987 0.988 0.988 0.988 0.988 0.989 0.989 Table 23B. Average bound and coverage percentage of 97.5% bootstrap for Student’s t process with  ,0 k  .10

0 0.90 SB

PB BCPB

0.890 0.923 0.939 0.942 0.945 0.951 0.959 0.962 0.902 0.933 0.948 0.953 0.953 0.957 0.964 0.965 0.913 0.942 0.955 0.960 0.960 0.965 0.968 0.968 0.870 0.907 0.926 0.935 0.939 0.944 0.954 0.957

0.847 0.861 0.868 0.872 0.877 0.879 0.883 0.887 0.842 0.858 0.866 0.870 0.876 0.879 0.883 0.887 0.837 0.856 0.864 0.869 0.875 0.878 0.882 0.887 0.853 0.865 0.870 0.873 0.878 0.880 0.884 0.888

0.95 SB

PB BCPB

0.860 0.899 0.906 0.920 0.930 0.941 0.948 0.953 0.875 0.913 0.917 0.934 0.939 0.946 0.954 0.957 0.887 0.924 0.928 0.941 0.944 0.952 0.958 0.960 0.834 0.881 0.892 0.910 0.919 0.930 0.944 0.947

0.921 0.929 0.933 0.935 0.937 0.939 0.941 0.943 0.918 0.927 0.931 0.934 0.936 0.938 0.941 0.943 0.915 0.925 0.930 0.932 0.936 0.938 0.94 0.942 0.925 0.931 0.934 0.936 0.938 0.94 0.942 0.943

0.99 SB

PB BCPB

0.856 0.889 0.907 0.914 0.925 0.933 0.944 0.950 0.871 0.903 0.921 0.924 0.935 0.942 0.951 0.954 0.887 0.911 0.929 0.933 0.942 0.949 0.956 0.957 0.832 0.872 0.895 0.898 0.917 0.923 0.936 0.941

0.984 0.986 0.986 0.987 0.987 0.988 0.988 0.989 0.984 0.985 0.986 0.987 0.987 0.987 0.988 0.988 0.983 0.985 0.986 0.986 0.987 0.987 0.988 0.988 0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989

Table 23B. (continued)

0.5 0.90 SB

PB BCPB

0.896 0.921 0.938 0.938 0.952 0.953 0.959 0.957 0.913 0.930 0.946 0.946 0.960 0.959 0.964 0.962 0.923 0.937 0.952 0.955 0.965 0.962 0.967 0.963 0.875 0.905 0.927 0.926 0.942 0.948 0.951 0.950

0.848 0.862 0.868 0.873 0.878 0.881 0.884 0.887 0.843 0.859 0.866 0.871 0.877 0.880 0.883 0.887 0.838 0.856 0.864 0.870 0.876 0.879 0.883 0.887 0.853 0.865 0.870 0.875 0.879 0.881 0.884 0.888

0.95 SB

PB BCPB0

0.875 0.906 0.921 0.936 0.944 0.946 0.951 0.955 0.892 0.920 0.934 0.943 0.949 0.953 0.958 0.959 0.901 0.931 0.942 0.952 0.955 0.957 0.960 0.960 0.852 0.887 0.904 0.923 0.933 0.936 0.944 0.952

0.923 0.929 0.933 0.935 0.938 0.939 0.941 0.943 0.921 0.927 0.932 0.934 0.937 0.939 0.941 0.943 0.918 0.926 0.931 0.933 0.936 0.938 0.941 0.943 0.927 0.931 0.935 0.936 0.939 0.940 0.942 0.943

0.99 SB

PB BCPB

0.869 0.894 0.919 0.927 0.936 0.942 0.946 0.956 0.887 0.907 0.932 0.936 0.943 0.949 0.953 0.963 0.898 0.915 0.942 0.944 0.949 0.955 0.959 0.967 0.847 0.878 0.901 0.910 0.925 0.934 0.937 0.950

0.984 0.986 0.987 0.987 0.987 0.988 0.988 0.989 0.984 0.985 0.986 0.987 0.987 0.988 0.988 0.989 0.983 0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989

1 0.90 SB

PB BCPB

0.898 0.929 0.944 0.939 0.949 0.954 0.957 0.965 0.910 0.940 0.950 0.949 0.957 0.960 0.962 0.968 0.918 0.947 0.953 0.956 0.962 0.966 0.964 0.971 0.879 0.917 0.929 0.930 0.943 0.946 0.951 0.962

0.854 0.865 0.872 0.875 0.880 0.882 0.886 0.889 0.850 0.863 0.870 0.874 0.879 0.882 0.885 0.888 0.846 0.861 0.869 0.873 0.878 0.881 0.885 0.888 0.858 0.868 0.873 0.877 0.881 0.883 0.886 0.889

0.95 SB

PB BCPB0

0.886 0.921 0.934 0.937 0.944 0.949 0.952 0.962 0.899 0.932 0.942 0.945 0.951 0.956 0.956 0.966 0.909 0.940 0.950 0.952 0.958 0.959 0.961 0.968 0.873 0.903 0.922 0.928 0.936 0.944 0.949 0.958

0.926 0.932 0.935 0.937 0.939 0.941 0.942 0.944 0.924 0.930 0.934 0.936 0.939 0.940 0.942 0.944 0.922 0.929 0.933 0.936 0.938 0.940 0.942 0.944 0.929 0.933 0.936 0.938 0.940 0.941 0.943 0.944

0.99 SB

PB BCPB

0.880 0.912 0.927 0.935 0.939 0.948 0.947 0.961 0.895 0.922 0.933 0.944 0.948 0.954 0.952 0.964 0.908 0.934 0.942 0.949 0.952 0.958 0.954 0.967 0.862 0.898 0.915 0.928 0.930 0.940 0.941 0.958

0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.984 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.989 Table 24A. Average bound and coverage percentage of 95% bootstrap for Student’s t process with  ,0 k  .20

T Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

0 0.90 SB

PB BCPB

0.858 0.891 0.905 0.917 0.920 0.927 0.933 0.941 0.870 0.902 0.913 0.926 0.928 0.933 0.935 0.944 0.883 0.913 0.925 0.934 0.934 0.940 0.941 0.948 0.836 0.879 0.891 0.908 0.907 0.921 0.927 0.937

0.857 0.868 0.874 0.877 0.881 0.883 0.887 0.890 0.854 0.867 0.872 0.876 0.881 0.883 0.886 0.889 0.850 0.864 0.871 0.875 0.880 0.882 0.886 0.889 0.860 0.870 0.875 0.878 0.882 0.884 0.887 0.890

0.95 SB

PB BCPB

0.847 0.879 0.892 0.906 0.909 0.917 0.921 0.928 0.862 0.888 0.901 0.915 0.917 0.924 0.927 0.933 0.873 0.900 0.914 0.928 0.926 0.933 0.934 0.941 0.829 0.869 0.879 0.895 0.901 0.911 0.915 0.924

0.927 0.933 0.936 0.938 0.940 0.941 0.943 0.945 0.926 0.932 0.936 0.937 0.940 0.941 0.942 0.944 0.923 0.931 0.935 0.937 0.939 0.941 0.942 0.944 0.929 0.934 0.937 0.939 0.940 0.942 0.943 0.945

0.99 SB

PB BCPB

0.835 0.869 0.888 0.901 0.911 0.919 0.917 0.923 0.855 0.880 0.899 0.909 0.917 0.927 0.921 0.926 0.874 0.893 0.910 0.919 0.926 0.938 0.927 0.929 0.815 0.857 0.880 0.890 0.903 0.911 0.909 0.917

0.985 0.987 0.987 0.987 0.988 0.988 0.989 0.989 0.985 0.986 0.987 0.987 0.988 0.988 0.989 0.989 0.984 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.989

0.5 0.90 SB

PB BCPB

0.858 0.901 0.910 0.910 0.926 0.932 0.936 0.934 0.872 0.912 0.917 0.916 0.931 0.936 0.940 0.937 0.885 0.924 0.929 0.926 0.938 0.944 0.947 0.940 0.841 0.888 0.903 0.903 0.917 0.925 0.931 0.930

0.857 0.868 0.874 0.878 0.882 0.884 0.887 0.890 0.854 0.866 0.873 0.877 0.881 0.883 0.887 0.889 0.850 0.864 0.871 0.875 0.880 0.883 0.886 0.889 0.860 0.870 0.875 0.879 0.882 0.884 0.887 0.890

0.95 SB

PB BCPB0

0.851 0.886 0.896 0.899 0.918 0.931 0.928 0.933 0.863 0.896 0.902 0.907 0.927 0.936 0.932 0.938 0.885 0.906 0.913 0.916 0.934 0.942 0.938 0.941 0.838 0.868 0.881 0.888 0.909 0.927 0.919 0.928

0.928 0.934 0.937 0.938 0.940 0.941 0.943 0.945 0.926 0.933 0.936 0.938 0.940 0.941 0.943 0.945 0.924 0.931 0.935 0.937 0.939 0.941 0.943 0.944 0.929 0.935 0.938 0.939 0.941 0.942 0.943 0.945

0.99 SB

PB BCPB

0.851 0.877 0.899 0.898 0.906 0.914 0.922 0.933 0.863 0.888 0.910 0.910 0.915 0.918 0.925 0.937 0.877 0.902 0.920 0.919 0.924 0.927 0.931 0.942 0.836 0.870 0.888 0.888 0.896 0.908 0.914 0.930

0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.989 0.985 0.987 0.987 0.988 0.988 0.988 0.989 0.989 0.985 0.986 0.987 0.987 0.988 0.988 0.989 0.989 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.989

Table 24A. (continued)

1 0.90 SB

PB BCPB

0.872 0.906 0.911 0.915 0.927 0.934 0.937 0.940 0.879 0.913 0.918 0.921 0.931 0.938 0.940 0.942 0.895 0.925 0.927 0.928 0.937 0.945 0.945 0.946 0.858 0.892 0.901 0.906 0.920 0.930 0.933 0.937

0.861 0.871 0.877 0.880 0.883 0.885 0.888 0.891 0.859 0.870 0.876 0.879 0.883 0.885 0.888 0.891 0.856 0.868 0.875 0.878 0.882 0.884 0.887 0.890 0.864 0.873 0.878 0.880 0.884 0.886 0.888 0.891

0.95 SB

PB BCPB

0.873 0.900 0.906 0.912 0.916 0.930 0.936 0.934 0.885 0.908 0.913 0.921 0.922 0.935 0.941 0.936 0.896 0.915 0.922 0.929 0.928 0.943 0.944 0.941 0.861 0.890 0.900 0.904 0.911 0.925 0.932 0.930

0.930 0.936 0.938 0.940 0.941 0.943 0.944 0.945 0.929 0.935 0.938 0.939 0.941 0.942 0.944 0.945 0.927 0.934 0.937 0.939 0.941 0.942 0.944 0.945 0.931 0.936 0.939 0.940 0.942 0.943 0.944 0.945

0.99 SB

PB BCPB

0.872 0.898 0.901 0.913 0.922 0.930 0.931 0.935 0.881 0.906 0.908 0.918 0.927 0.935 0.934 0.936 0.894 0.915 0.915 0.927 0.935 0.940 0.939 0.940 0.855 0.885 0.891 0.906 0.915 0.924 0.925 0.932

0.986 0.987 0.988 0.988 0.988 0.989 0.989 0.989 0.986 0.987 0.988 0.988 0.988 0.988 0.989 0.989 0.985 0.987 0.987 0.988 0.988 0.988 0.989 0.989 0.986 0.987 0.988 0.988 0.988 0.989 0.989 0.989 Table24B. Average bound and coverage percentage of 97.5% bootstrap for Student’s t process with  ,0 k  .20

T Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

0 0.90 SB

PB BCPB

0.894 0.929 0.941 0.946 0.948 0.949 0.961 0.967 0.910 0.939 0.949 0.956 0.955 0.955 0.967 0.971 0.922 0.945 0.957 0.960 0.959 0.962 0.970 0.972 0.87 0.916 0.933 0.936 0.938 0.941 0.954 0.962

0.849 0.862 0.869 0.873 0.878 0.881 0.884 0.888 0.844 0.859 0.867 0.871 0.877 0.88 0.883 0.887 0.839 0.857 0.865 0.870 0.876 0.879 0.883 0.887 0.854 0.865 0.871 0.874 0.879 0.882 0.884 0.888

0.95 SB

PB BCPB

0.883 0.911 0.923 0.939 0.944 0.949 0.951 0.957 0.897 0.923 0.933 0.947 0.950 0.955 0.957 0.960 0.910 0.930 0.943 0.953 0.955 0.960 0.962 0.963 0.857 0.894 0.911 0.925 0.933 0.943 0.947 0.953

0.922 0.930 0.933 0.935 0.938 0.940 0.941 0.943 0.920 0.929 0.932 0.934 0.938 0.939 0.941 0.943 0.917 0.927 0.931 0.934 0.937 0.939 0.941 0.943 0.926 0.932 0.935 0.936 0.939 0.940 0.942 0.944

0.99 SB

PB BCPB

0.880 0.909 0.922 0.931 0.931 0.947 0.95 0.957 0.894 0.920 0.934 0.941 0.940 0.957 0.955 0.962 0.907 0.931 0.941 0.945 0.944 0.961 0.960 0.963 0.859 0.891 0.905 0.919 0.922 0.934 0.945 0.951

0.984 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.984 0.986 0.986 0.987 0.987 0.988 0.988 0.989 0.983 0.985 0.986 0.987 0.987 0.988 0.988 0.989 0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989

0.5 0.90 SB

PB BCPB

0.904 0.933 0.941 0.947 0.953 0.956 0.958 0.963 0.915 0.942 0.951 0.956 0.960 0.961 0.963 0.969 0.930 0.950 0.958 0.960 0.965 0.963 0.964 0.970 0.882 0.917 0.932 0.938 0.949 0.951 0.950 0.958

0.849 0.863 0.869 0.873 0.878 0.881 0.884 0.888 0.844 0.860 0.867 0.872 0.877 0.880 0.884 0.888 0.840 0.858 0.866 0.870 0.876 0.880 0.884 0.887 0.854 0.866 0.871 0.875 0.879 0.882 0.885 0.888

0.95 SB

PB BCPB0

0.884 0.923 0.930 0.938 0.946 0.955 0.954 0.960 0.899 0.932 0.939 0.947 0.953 0.963 0.958 0.965 0.912 0.941 0.945 0.954 0.959 0.967 0.963 0.967 0.864 0.906 0.916 0.928 0.939 0.949 0.946 0.955

0.924 0.931 0.934 0.936 0.938 0.94 0.942 0.944 0.921 0.929 0.933 0.935 0.938 0.939 0.941 0.943 0.919 0.928 0.932 0.934 0.937 0.939 0.941 0.943 0.927 0.932 0.935 0.937 0.939 0.94 0.942 0.944

0.99 SB

PB BCPB

0.878 0.913 0.925 0.935 0.940 0.947 0.953 0.960 0.896 0.928 0.941 0.944 0.950 0.953 0.958 0.964 0.908 0.933 0.947 0.953 0.956 0.960 0.962 0.967 0.851 0.904 0.914 0.921 0.931 0.941 0.949 0.955

0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.984 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.984 0.985 0.986 0.987 0.987 0.988 0.988 0.989 0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989

1 0.90 SB

PB BCPB

0.909 0.933 0.945 0.945 0.954 0.960 0.968 0.971 0.920 0.942 0.951 0.952 0.960 0.965 0.971 0.973 0.930 0.951 0.955 0.958 0.964 0.967 0.974 0.975 0.889 0.921 0.929 0.938 0.948 0.952 0.963 0.969

0.853 0.866 0.872 0.876 0.880 0.883 0.886 0.889 0.849 0.864 0.871 0.875 0.879 0.882 0.885 0.889 0.846 0.862 0.869 0.874 0.878 0.881 0.885 0.888 0.857 0.869 0.874 0.877 0.881 0.883 0.886 0.889

0.95 SB

PB BCPB0

0.907 0.928 0.94 0.949 0.951 0.957 0.961 0.963 0.918 0.941 0.949 0.954 0.956 0.961 0.967 0.967 0.928 0.947 0.955 0.959 0.960 0.965 0.970 0.968 0.886 0.915 0.930 0.938 0.942 0.952 0.956 0.959

0.927 0.933 0.936 0.938 0.940 0.941 0.943 0.944 0.925 0.932 0.935 0.937 0.940 0.941 0.942 0.944 0.923 0.931 0.934 0.936 0.939 0.941 0.942 0.944 0.929 0.934 0.937 0.938 0.940 0.942 0.943 0.945

0.99 SB

PB BCPB

0.897 0.931 0.939 0.945 0.949 0.958 0.958 0.961 0.908 0.937 0.945 0.949 0.954 0.962 0.964 0.965 0.916 0.944 0.952 0.956 0.961 0.966 0.965 0.966 0.882 0.917 0.930 0.937 0.940 0.952 0.952 0.958

0.985 0.987 0.987 0.988 0.988 0.988 0.989 0.989 0.985 0.986 0.987 0.987 0.988 0.988 0.989 0.989 0.985 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.986 0.987 0.987 0.988 0.988 0.988 0.989 0.989

Table 25A. Average bound and coverage percentage of 95% bootstrap for Chi-squared process with  ,0 k  .12

T Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

12 0.75 SB

PB BCPB

0.906 0.925 0.932 0.936 0.934 0.944 0.936 0.948 0.914 0.931 0.937 0.941 0.937 0.945 0.940 0.950 0.925 0.940 0.943 0.947 0.941 0.948 0.945 0.952 0.896 0.916 0.927 0.930 0.931 0.941 0.933 0.946

0.662 0.687 0.699 0.705 0.713 0.718 0.724 0.729 0.659 0.685 0.698 0.705 0.712 0.718 0.724 0.729 0.655 0.683 0.696 0.703 0.711 0.717 0.724 0.729 0.666 0.688 0.700 0.706 0.713 0.719 0.725 0.730

0.80 SB

PB BCPB

0.900 0.919 0.926 0.927 0.931 0.934 0.936 0.938 0.910 0.925 0.932 0.935 0.935 0.937 0.940 0.940 0.921 0.936 0.941 0.943 0.940 0.940 0.942 0.944 0.884 0.912 0.918 0.923 0.927 0.930 0.935 0.936

0.726 0.748 0.757 0.763 0.769 0.773 0.778 0.783 0.723 0.746 0.756 0.762 0.768 0.773 0.778 0.783 0.719 0.744 0.754 0.761 0.768 0.772 0.778 0.783 0.730 0.750 0.758 0.764 0.770 0.774 0.779 0.783

0.85 SB

PB BCPB

0.880 0.899 0.914 0.919 0.928 0.936 0.937 0.939 0.891 0.908 0.921 0.924 0.932 0.940 0.941 0.943 0.906 0.920 0.930 0.931 0.938 0.944 0.947 0.945 0.867 0.891 0.908 0.914 0.923 0.932 0.934 0.936

0.792 0.808 0.815 0.820 0.826 0.828 0.833 0.837 0.789 0.806 0.814 0.819 0.825 0.828 0.832 0.836 0.784 0.804 0.812 0.818 0.824 0.827 0.832 0.836 0.796 0.810 0.817 0.821 0.826 0.829 0.833 0.837 12.5 0.75 SB

PB BCPB

0.908 0.921 0.932 0.934 0.938 0.940 0.937 0.948 0.916 0.927 0.937 0.940 0.942 0.944 0.938 0.950 0.924 0.938 0.945 0.944 0.945 0.945 0.941 0.953 0.897 0.914 0.927 0.929 0.934 0.939 0.934 0.947

0.665 0.688 0.699 0.706 0.714 0.719 0.724 0.730 0.662 0.686 0.698 0.705 0.713 0.718 0.724 0.730 0.657 0.684 0.696 0.704 0.712 0.718 0.724 0.729 0.668 0.689 0.700 0.707 0.714 0.719 0.725 0.730

0.80 SB

PB BCPB0

0.903 0.919 0.923 0.924 0.935 0.927 0.940 0.942 0.910 0.928 0.927 0.927 0.938 0.931 0.943 0.946 0.920 0.934 0.936 0.933 0.943 0.936 0.946 0.948 0.888 0.909 0.917 0.917 0.931 0.925 0.938 0.941

0.728 0.749 0.757 0.763 0.770 0.774 0.779 0.783 0.725 0.747 0.756 0.763 0.769 0.774 0.778 0.783 0.721 0.745 0.755 0.761 0.769 0.773 0.778 0.782 0.731 0.751 0.759 0.764 0.771 0.775 0.779 0.783

0.85 SB

PB BCPB

0.881 0.905 0.917 0.926 0.929 0.932 0.935 0.938 0.891 0.910 0.923 0.929 0.934 0.937 0.939 0.942 0.907 0.918 0.929 0.936 0.937 0.941 0.941 0.945 0.873 0.897 0.909 0.916 0.923 0.927 0.933 0.936

0.794 0.810 0.817 0.821 0.826 0.829 0.833 0.837 0.791 0.808 0.816 0.820 0.826 0.829 0.832 0.837 0.787 0.806 0.814 0.819 0.825 0.828 0.832 0.836 0.797 0.812 0.818 0.822 0.827 0.830 0.833 0.837

13 0.75 SB

PB BCPB

0.910 0.922 0.929 0.939 0.938 0.941 0.934 0.944 0.917 0.927 0.933 0.940 0.943 0.943 0.934 0.946 0.925 0.930 0.940 0.946 0.946 0.945 0.938 0.947 0.897 0.915 0.923 0.933 0.933 0.937 0.932 0.941

0.666 0.689 0.700 0.706 0.714 0.719 0.725 0.730 0.663 0.687 0.699 0.706 0.713 0.718 0.724 0.730 0.658 0.685 0.697 0.705 0.712 0.718 0.724 0.730 0.669 0.690 0.701 0.707 0.714 0.719 0.725 0.731

0.80 SB

PB BCPB0

0.902 0.918 0.923 0.929 0.934 0.939 0.937 0.941 0.911 0.927 0.930 0.934 0.938 0.943 0.939 0.945 0.918 0.936 0.936 0.939 0.944 0.947 0.944 0.948 0.895 0.910 0.915 0.921 0.929 0.938 0.934 0.940

0.728 0.748 0.758 0.764 0.770 0.774 0.779 0.783 0.725 0.746 0.757 0.763 0.769 0.774 0.779 0.783 0.721 0.744 0.756 0.762 0.769 0.773 0.778 0.783 0.731 0.750 0.759 0.765 0.77 0.775 0.779 0.783

0.85 SB

PB BCPB

0.885 0.914 0.914 0.926 0.928 0.933 0.938 0.935 0.891 0.921 0.917 0.932 0.931 0.939 0.941 0.939 0.903 0.931 0.925 0.940 0.935 0.944 0.945 0.944 0.874 0.904 0.908 0.921 0.923 0.928 0.934 0.932

0.796 0.81 0.817 0.822 0.827 0.830 0.833 0.837 0.793 0.808 0.816 0.821 0.827 0.829 0.833 0.837 0.789 0.806 0.815 0.820 0.826 0.829 0.833 0.837 0.799 0.812 0.819 0.823 0.828 0.830 0.833 0.837 11.5 0.75 SB

PB BCPB

0.902 0.922 0.930 0.932 0.930 0.938 0.945 0.948 0.915 0.928 0.936 0.935 0.933 0.941 0.949 0.948 0.925 0.936 0.944 0.941 0.938 0.945 0.953 0.951 0.893 0.916 0.925 0.927 0.927 0.936 0.942 0.945

0.663 0.686 0.697 0.705 0.712 0.717 0.723 0.729 0.659 0.685 0.696 0.704 0.712 0.717 0.723 0.729 0.655 0.682 0.695 0.702 0.711 0.716 0.723 0.729 0.666 0.688 0.698 0.706 0.713 0.718 0.724 0.730

0.80 SB

PB BCPB0

0.899 0.915 0.921 0.929 0.929 0.938 0.938 0.942 0.911 0.919 0.927 0.934 0.933 0.943 0.941 0.945 0.926 0.927 0.933 0.939 0.936 0.947 0.944 0.947 0.886 0.905 0.914 0.924 0.924 0.934 0.936 0.94

0.725 0.747 0.757 0.763 0.768 0.773 0.778 0.783 0.722 0.745 0.756 0.762 0.768 0.773 0.778 0.783 0.717 0.743 0.755 0.760 0.767 0.772 0.777 0.782 0.729 0.749 0.759 0.764 0.769 0.773 0.778 0.783

0.85 SB

PB BCPB

0.880 0.904 0.914 0.921 0.927 0.934 0.934 0.935 0.891 0.912 0.922 0.930 0.930 0.939 0.939 0.937 0.905 0.922 0.932 0.938 0.936 0.944 0.943 0.941 0.869 0.891 0.906 0.915 0.923 0.930 0.932 0.933

0.791 0.808 0.815 0.820 0.825 0.828 0.832 0.836 0.788 0.806 0.813 0.819 0.824 0.828 0.832 0.836 0.783 0.803 0.812 0.818 0.824 0.827 0.831 0.836 0.795 0.810 0.816 0.821 0.826 0.829 0.832 0.836

Table 25A. (continued)

11 0.75 SB

PB BCPB

0.903 0.918 0.928 0.931 0.935 0.938 0.937 0.945 0.909 0.925 0.933 0.936 0.938 0.939 0.939 0.947 0.921 0.934 0.94 0.941 0.942 0.943 0.942 0.950 0.886 0.908 0.920 0.926 0.932 0.934 0.935 0.943

0.662 0.686 0.696 0.704 0.712 0.717 0.723 0.729 0.659 0.684 0.695 0.703 0.711 0.717 0.723 0.729 0.654 0.682 0.693 0.702 0.710 0.716 0.723 0.729 0.666 0.688 0.697 0.705 0.713 0.718 0.724 0.729

0.80 SB

PB BCPB

0.893 0.91 0.916 0.924 0.931 0.931 0.937 0.942 0.904 0.918 0.922 0.929 0.936 0.933 0.942 0.946 0.916 0.928 0.934 0.937 0.941 0.938 0.943 0.947 0.884 0.901 0.910 0.917 0.928 0.928 0.934 0.940

0.726 0.746 0.757 0.762 0.768 0.773 0.778 0.783 0.722 0.745 0.755 0.761 0.767 0.772 0.778 0.782 0.717 0.742 0.754 0.760 0.767 0.772 0.777 0.782 0.729 0.748 0.758 0.763 0.769 0.773 0.778 0.783

0.85 SB

PB BCPB

0.874 0.906 0.914 0.919 0.927 0.929 0.934 0.938 0.885 0.915 0.921 0.926 0.932 0.934 0.938 0.942 0.899 0.930 0.930 0.936 0.938 0.940 0.943 0.946 0.862 0.894 0.907 0.912 0.921 0.924 0.929 0.936

0.791 0.807 0.814 0.819 0.824 0.827 0.832 0.836 0.788 0.805 0.812 0.818 0.824 0.827 0.831 0.835 0.783 0.802 0.810 0.816 0.823 0.826 0.831 0.835 0.795 0.809 0.815 0.820 0.825 0.828 0.832 0.836 Table 25B. Average bound and coverage percentage of 97.5% bootstrap for Chi-squared process with  ,0 k  .12

T Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

12 0.75 SB

PB BCPB

0.941 0.953 0.957 0.961 0.961 0.961 0.966 0.97 0.952 0.960 0.963 0.964 0.965 0.964 0.969 0.972 0.958 0.966 0.969 0.968 0.967 0.968 0.971 0.975 0.928 0.946 0.950 0.956 0.958 0.959 0.964 0.969

0.646 0.675 0.690 0.697 0.707 0.712 0.719 0.726 0.640 0.672 0.688 0.695 0.706 0.711 0.719 0.726 0.636 0.670 0.686 0.694 0.705 0.711 0.718 0.726 0.651 0.678 0.692 0.698 0.708 0.713 0.720 0.726

0.80 SB

PB BCPB

0.932 0.944 0.954 0.955 0.960 0.961 0.965 0.968 0.939 0.949 0.960 0.961 0.963 0.965 0.967 0.970 0.946 0.955 0.964 0.966 0.967 0.967 0.969 0.972 0.916 0.935 0.947 0.950 0.956 0.958 0.961 0.966

0.715 0.737 0.749 0.755 0.763 0.769 0.775 0.780 0.710 0.734 0.747 0.754 0.762 0.768 0.774 0.780 0.705 0.732 0.746 0.753 0.762 0.767 0.774 0.779 0.721 0.740 0.751 0.757 0.765 0.769 0.775 0.780

0.85 SB

PB BCPB

0.911 0.932 0.945 0.950 0.959 0.959 0.963 0.966 0.918 0.940 0.955 0.954 0.964 0.964 0.968 0.970 0.926 0.945 0.961 0.959 0.967 0.967 0.971 0.972 0.891 0.918 0.933 0.940 0.951 0.953 0.958 0.962

0.783 0.801 0.809 0.814 0.821 0.824 0.829 0.834 0.778 0.798 0.807 0.813 0.820 0.824 0.829 0.834 0.773 0.795 0.806 0.812 0.819 0.823 0.828 0.833 0.788 0.804 0.811 0.816 0.822 0.825 0.830 0.834 12.5 0.75 SB

PB BCPB

0.936 0.952 0.958 0.962 0.966 0.967 0.973 0.971 0.944 0.958 0.965 0.965 0.970 0.968 0.975 0.973 0.951 0.963 0.969 0.968 0.971 0.973 0.977 0.974 0.923 0.945 0.951 0.957 0.962 0.962 0.970 0.970

0.646 0.676 0.690 0.698 0.706 0.712 0.719 0.726 0.641 0.673 0.689 0.696 0.705 0.712 0.719 0.726 0.637 0.671 0.687 0.695 0.705 0.711 0.718 0.726 0.652 0.679 0.692 0.699 0.707 0.713 0.720 0.727

0.80 SB

PB BCPB0

0.930 0.944 0.952 0.963 0.964 0.966 0.968 0.968 0.941 0.950 0.959 0.967 0.968 0.969 0.970 0.970 0.949 0.956 0.965 0.970 0.973 0.971 0.972 0.972 0.915 0.932 0.946 0.958 0.957 0.963 0.966 0.968

0.715 0.739 0.749 0.756 0.763 0.769 0.774 0.780 0.710 0.736 0.747 0.755 0.763 0.768 0.774 0.780 0.706 0.734 0.746 0.753 0.762 0.768 0.774 0.780 0.721 0.742 0.751 0.758 0.765 0.770 0.775 0.781

0.85 SB

PB BCPB

0.921 0.940 0.947 0.959 0.961 0.965 0.967 0.968 0.929 0.948 0.953 0.964 0.966 0.969 0.970 0.972 0.936 0.953 0.959 0.966 0.968 0.972 0.971 0.973 0.902 0.930 0.942 0.953 0.955 0.959 0.963 0.966

0.782 0.801 0.810 0.814 0.821 0.825 0.830 0.834 0.777 0.799 0.808 0.813 0.820 0.825 0.829 0.834 0.773 0.796 0.807 0.812 0.820 0.824 0.829 0.834 0.788 0.804 0.812 0.816 0.822 0.826 0.83 0.835

13 0.75 SB

PB BCPB

0.942 0.948 0.955 0.958 0.964 0.968 0.970 0.973 0.949 0.955 0.960 0.963 0.968 0.970 0.972 0.974 0.955 0.961 0.964 0.966 0.970 0.972 0.972 0.974 0.929 0.939 0.951 0.951 0.960 0.967 0.968 0.971

0.648 0.678 0.691 0.698 0.708 0.712 0.720 0.727 0.643 0.675 0.689 0.697 0.707 0.712 0.719 0.726 0.639 0.673 0.688 0.696 0.706 0.711 0.719 0.726 0.654 0.681 0.693 0.700 0.709 0.713 0.720 0.727

0.80 SB

PB BCPB0

0.927 0.946 0.956 0.956 0.962 0.964 0.968 0.968 0.937 0.954 0.962 0.962 0.967 0.966 0.970 0.971 0.945 0.960 0.966 0.965 0.969 0.968 0.972 0.972 0.914 0.932 0.947 0.951 0.957 0.959 0.965 0.967

0.714 0.739 0.750 0.757 0.763 0.77 0.775 0.781 0.709 0.736 0.748 0.755 0.762 0.769 0.774 0.780 0.705 0.734 0.747 0.754 0.762 0.768 0.774 0.780 0.719 0.742 0.752 0.758 0.764 0.770 0.775 0.781

0.85 SB

PB BCPB

0.920 0.942 0.950 0.954 0.960 0.963 0.966 0.968 0.931 0.949 0.957 0.959 0.967 0.967 0.968 0.970 0.939 0.955 0.962 0.964 0.970 0.968 0.971 0.972 0.902 0.931 0.940 0.949 0.957 0.957 0.963 0.966

0.784 0.802 0.811 0.815 0.822 0.826 0.830 0.835 0.780 0.800 0.809 0.814 0.821 0.825 0.830 0.834 0.776 0.798 0.808 0.813 0.820 0.825 0.829 0.834 0.789 0.805 0.813 0.817 0.823 0.827 0.831 0.835

Table 25B. (continued) 11.5 0.75 SB

PB BCPB

0.934 0.952 0.955 0.957 0.964 0.964 0.968 0.970 0.949 0.957 0.958 0.963 0.967 0.966 0.971 0.972 0.955 0.961 0.962 0.965 0.970 0.969 0.972 0.974 0.921 0.946 0.947 0.951 0.960 0.961 0.965 0.968

0.644 0.673 0.688 0.697 0.705 0.711 0.718 0.726 0.639 0.670 0.686 0.695 0.704 0.711 0.718 0.726 0.634 0.668 0.684 0.694 0.704 0.710 0.717 0.725 0.650 0.676 0.690 0.698 0.706 0.712 0.719 0.726

0.80 SB

PB BCPB

0.929 0.945 0.953 0.955 0.962 0.964 0.965 0.967 0.938 0.951 0.959 0.959 0.969 0.967 0.969 0.969 0.946 0.955 0.963 0.964 0.972 0.969 0.972 0.970 0.914 0.934 0.945 0.951 0.958 0.960 0.962 0.963

0.711 0.737 0.748 0.755 0.763 0.767 0.774 0.780 0.706 0.734 0.746 0.754 0.762 0.767 0.773 0.780 0.701 0.731 0.744 0.752 0.761 0.766 0.773 0.779 0.718 0.740 0.750 0.757 0.764 0.768 0.774 0.780

0.85 SB

PB BCPB

0.909 0.940 0.948 0.952 0.956 0.961 0.961 0.965 0.920 0.950 0.954 0.958 0.960 0.964 0.964 0.967 0.928 0.955 0.960 0.966 0.964 0.966 0.967 0.969 0.892 0.93 0.941 0.947 0.951 0.956 0.956 0.962

0.780 0.798 0.808 0.813 0.820 0.824 0.829 0.834 0.774 0.795 0.806 0.811 0.819 0.823 0.828 0.833 0.770 0.793 0.804 0.810 0.818 0.822 0.828 0.833 0.786 0.802 0.810 0.814 0.821 0.825 0.829 0.834

11 0.75 SB

PB BCPB

0.931 0.953 0.956 0.959 0.964 0.967 0.968 0.970 0.939 0.959 0.962 0.964 0.967 0.970 0.972 0.972 0.949 0.963 0.965 0.967 0.969 0.971 0.974 0.972 0.919 0.944 0.951 0.954 0.957 0.964 0.966 0.967

0.642 0.672 0.686 0.696 0.705 0.711 0.718 0.726 0.637 0.669 0.684 0.694 0.704 0.710 0.717 0.725 0.632 0.667 0.683 0.693 0.704 0.709 0.717 0.725 0.649 0.676 0.688 0.698 0.707 0.712 0.718 0.726

0.80 SB

PB BCPB0

0.927 0.948 0.954 0.957 0.962 0.963 0.967 0.968 0.940 0.954 0.960 0.962 0.968 0.968 0.969 0.971 0.946 0.959 0.964 0.968 0.972 0.972 0.970 0.972 0.914 0.938 0.943 0.952 0.956 0.959 0.963 0.966

0.711 0.736 0.747 0.754 0.763 0.767 0.773 0.779 0.706 0.733 0.745 0.753 0.762 0.766 0.772 0.779 0.701 0.731 0.744 0.751 0.761 0.766 0.772 0.778 0.718 0.740 0.750 0.756 0.764 0.768 0.774 0.779

0.85 SB

PB BCPB

0.904 0.924 0.941 0.952 0.959 0.955 0.963 0.966 0.916 0.936 0.953 0.960 0.966 0.959 0.966 0.968 0.923 0.947 0.959 0.966 0.969 0.963 0.969 0.969 0.881 0.913 0.928 0.946 0.950 0.949 0.957 0.963

0.779 0.798 0.808 0.812 0.819 0.824 0.828 0.833 0.774 0.795 0.806 0.810 0.817 0.823 0.828 0.833 0.769 0.792 0.804 0.809 0.817 0.822 0.827 0.832 0.786 0.801 0.810 0.814 0.820 0.824 0.829 0.834 Table 26A. Average bound and coverage percentage of 95% bootstrap for Chi-squared process with  ,0 k  .15

T Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

15 0.75 SB

PB BCPB

0.907 0.933 0.929 0.935 0.938 0.937 0.939 0.944 0.916 0.939 0.936 0.939 0.939 0.940 0.942 0.945 0.926 0.946 0.941 0.942 0.943 0.943 0.945 0.948 0.899 0.927 0.923 0.930 0.936 0.934 0.938 0.941

0.662 0.684 0.698 0.705 0.713 0.718 0.724 0.730 0.659 0.683 0.697 0.704 0.712 0.718 0.724 0.729 0.654 0.680 0.695 0.703 0.712 0.717 0.723 0.729 0.666 0.686 0.699 0.706 0.714 0.718 0.724 0.730

0.80 SB

PB BCPB

0.894 0.921 0.926 0.925 0.932 0.931 0.937 0.946 0.907 0.926 0.930 0.930 0.935 0.934 0.939 0.949 0.924 0.936 0.936 0.937 0.941 0.939 0.942 0.951 0.878 0.912 0.918 0.921 0.925 0.925 0.932 0.943

0.727 0.746 0.757 0.763 0.769 0.774 0.778 0.783 0.723 0.745 0.755 0.762 0.768 0.773 0.778 0.782 0.719 0.742 0.754 0.761 0.767 0.773 0.777 0.782 0.730 0.748 0.758 0.764 0.770 0.774 0.779 0.783

0.85 SB

PB BCPB

0.884 0.905 0.920 0.919 0.934 0.938 0.937 0.936 0.894 0.916 0.928 0.924 0.939 0.942 0.940 0.938 0.905 0.926 0.935 0.932 0.944 0.948 0.945 0.942 0.871 0.896 0.914 0.909 0.926 0.934 0.931 0.930

0.791 0.807 0.815 0.820 0.826 0.828 0.832 0.837 0.788 0.805 0.814 0.819 0.825 0.828 0.832 0.836 0.783 0.803 0.812 0.818 0.824 0.827 0.831 0.836 0.794 0.809 0.816 0.821 0.826 0.829 0.832 0.837 15.5 0.75 SB

PB BCPB

0.901 0.926 0.928 0.937 0.935 0.938 0.935 0.939 0.910 0.930 0.933 0.941 0.938 0.941 0.938 0.941 0.923 0.937 0.938 0.947 0.942 0.943 0.941 0.944 0.893 0.919 0.922 0.932 0.931 0.935 0.933 0.937

0.665 0.687 0.698 0.705 0.713 0.718 0.725 0.730 0.662 0.685 0.697 0.705 0.713 0.718 0.724 0.730 0.658 0.683 0.696 0.703 0.712 0.717 0.724 0.730 0.669 0.688 0.699 0.706 0.714 0.719 0.725 0.730

0.80 SB

PB BCPB0

0.903 0.911 0.921 0.930 0.933 0.940 0.944 0.940 0.912 0.918 0.926 0.934 0.937 0.944 0.948 0.942 0.923 0.928 0.933 0.94 0.943 0.948 0.951 0.944 0.890 0.902 0.915 0.925 0.927 0.935 0.940 0.938

0.727 0.748 0.757 0.763 0.769 0.773 0.778 0.783 0.724 0.746 0.756 0.762 0.768 0.773 0.778 0.783 0.719 0.744 0.755 0.760 0.768 0.772 0.778 0.783 0.730 0.750 0.759 0.764 0.770 0.774 0.779 0.783

0.85 SB

PB BCPB

0.885 0.910 0.919 0.923 0.930 0.932 0.935 0.939 0.894 0.918 0.928 0.931 0.933 0.934 0.940 0.942 0.907 0.930 0.934 0.938 0.942 0.939 0.943 0.943 0.873 0.903 0.908 0.916 0.923 0.928 0.932 0.937

0.794 0.809 0.817 0.820 0.827 0.829 0.833 0.837 0.791 0.807 0.816 0.819 0.826 0.829 0.832 0.837 0.787 0.805 0.814 0.818 0.825 0.828 0.832 0.836 0.797 0.811 0.818 0.821 0.827 0.829 0.833 0.837

Table 26A. (continued)

16 0.75 SB

PB BCPB

0.903 0.930 0.932 0.934 0.937 0.934 0.941 0.943 0.914 0.934 0.938 0.936 0.940 0.936 0.942 0.944 0.923 0.942 0.944 0.942 0.945 0.938 0.943 0.946 0.890 0.921 0.929 0.929 0.934 0.929 0.939 0.940

0.663 0.688 0.699 0.706 0.713 0.719 0.724 0.730 0.660 0.686 0.698 0.705 0.712 0.718 0.724 0.730 0.656 0.684 0.696 0.704 0.711 0.718 0.724 0.730 0.666 0.690 0.700 0.707 0.713 0.719 0.725 0.730

0.80 SB

PB BCPB

0.900 0.923 0.928 0.935 0.933 0.940 0.939 0.944 0.909 0.928 0.931 0.939 0.936 0.943 0.941 0.947 0.920 0.938 0.937 0.944 0.942 0.948 0.943 0.949 0.889 0.912 0.922 0.928 0.928 0.937 0.935 0.940

0.727 0.747 0.758 0.763 0.770 0.774 0.779 0.784 0.724 0.745 0.757 0.762 0.769 0.773 0.778 0.783 0.719 0.743 0.755 0.761 0.768 0.773 0.778 0.783 0.730 0.749 0.759 0.764 0.770 0.774 0.779 0.784

0.85 SB

PB BCPB

0.879 0.912 0.920 0.926 0.930 0.926 0.941 0.941 0.893 0.919 0.928 0.933 0.937 0.930 0.944 0.942 0.907 0.928 0.935 0.940 0.942 0.936 0.950 0.945 0.863 0.905 0.911 0.918 0.924 0.923 0.938 0.939

0.795 0.810 0.817 0.821 0.826 0.830 0.833 0.837 0.792 0.808 0.816 0.820 0.826 0.829 0.832 0.837 0.788 0.806 0.814 0.819 0.825 0.829 0.832 0.837 0.799 0.811 0.818 0.822 0.827 0.830 0.833 0.837 14.5 0.75 SB

PB BCPB

0.907 0.925 0.928 0.932 0.942 0.946 0.946 0.946 0.915 0.931 0.931 0.937 0.944 0.947 0.947 0.947 0.924 0.939 0.939 0.942 0.946 0.951 0.951 0.948 0.894 0.919 0.922 0.929 0.938 0.944 0.944 0.944

0.662 0.686 0.698 0.704 0.712 0.717 0.723 0.729 0.658 0.684 0.697 0.703 0.712 0.716 0.723 0.729 0.654 0.682 0.695 0.702 0.711 0.716 0.723 0.729 0.665 0.688 0.699 0.705 0.713 0.717 0.724 0.729

0.80 SB

PB BCPB0

0.901 0.916 0.922 0.930 0.933 0.938 0.939 0.942 0.910 0.924 0.929 0.935 0.936 0.941 0.941 0.944 0.918 0.930 0.937 0.943 0.938 0.946 0.944 0.945 0.886 0.911 0.915 0.922 0.929 0.936 0.937 0.939

0.727 0.746 0.757 0.761 0.769 0.772 0.778 0.783 0.724 0.745 0.756 0.760 0.768 0.772 0.778 0.782 0.719 0.742 0.754 0.759 0.768 0.771 0.777 0.782 0.731 0.748 0.758 0.762 0.770 0.773 0.778 0.783

0.85 SB

PB BCPB

0.888 0.907 0.918 0.923 0.928 0.932 0.932 0.941 0.901 0.916 0.927 0.929 0.934 0.938 0.939 0.945 0.909 0.923 0.937 0.937 0.943 0.943 0.940 0.947 0.877 0.897 0.912 0.917 0.920 0.926 0.927 0.938

0.789 0.808 0.814 0.819 0.825 0.828 0.832 0.836 0.786 0.806 0.813 0.818 0.824 0.828 0.832 0.836 0.781 0.803 0.811 0.817 0.823 0.827 0.831 0.835 0.793 0.809 0.816 0.820 0.825 0.829 0.832 0.836

14 0.75 SB

PB BCPB

0.900 0.926 0.931 0.935 0.938 0.944 0.940 0.943 0.907 0.931 0.936 0.938 0.942 0.948 0.941 0.946 0.920 0.936 0.941 0.943 0.947 0.950 0.942 0.947 0.888 0.915 0.924 0.930 0.935 0.941 0.937 0.941

0.662 0.685 0.697 0.704 0.712 0.717 0.723 0.729 0.659 0.683 0.695 0.703 0.712 0.716 0.723 0.729 0.654 0.681 0.694 0.702 0.711 0.716 0.722 0.729 0.666 0.687 0.698 0.705 0.713 0.717 0.724 0.729

0.80 SB

PB BCPB0

0.894 0.894 0.927 0.935 0.936 0.926 0.939 0.941 0.905 0.905 0.932 0.941 0.941 0.930 0.942 0.943 0.917 0.917 0.942 0.948 0.945 0.935 0.944 0.945 0.884 0.884 0.921 0.929 0.931 0.923 0.935 0.938

0.724 0.747 0.756 0.760 0.769 0.773 0.778 0.783 0.721 0.745 0.754 0.759 0.768 0.772 0.777 0.783 0.716 0.742 0.753 0.758 0.767 0.772 0.777 0.782 0.728 0.749 0.757 0.761 0.769 0.773 0.778 0.783

0.85 SB

PB BCPB

0.882 0.896 0.916 0.924 0.925 0.935 0.936 0.938 0.891 0.904 0.926 0.930 0.932 0.938 0.941 0.940 0.905 0.917 0.933 0.939 0.938 0.943 0.944 0.942 0.868 0.882 0.908 0.918 0.919 0.930 0.931 0.935

0.790 0.808 0.814 0.819 0.824 0.827 0.831 0.836 0.787 0.806 0.813 0.817 0.823 0.827 0.831 0.835 0.782 0.804 0.811 0.816 0.822 0.826 0.831 0.835 0.794 0.810 0.815 0.820 0.825 0.828 0.832 0.836 Table 26B. Average bound and coverage percentage of 97.5% bootstrap for Chi-squared process with  ,0 k  .15

T Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

15 0.75 SB

PB BCPB

0.943 0.954 0.961 0.960 0.965 0.969 0.969 0.970 0.950 0.960 0.966 0.965 0.969 0.973 0.970 0.972 0.959 0.967 0.971 0.967 0.972 0.976 0.971 0.972 0.928 0.943 0.954 0.956 0.961 0.965 0.965 0.968

0.644 0.674 0.689 0.696 0.706 0.711 0.719 0.726 0.639 0.671 0.687 0.695 0.705 0.710 0.718 0.726 0.635 0.669 0.686 0.694 0.704 0.710 0.718 0.725 0.650 0.677 0.691 0.698 0.707 0.712 0.719 0.726

0.80 SB

PB BCPB

0.922 0.949 0.957 0.952 0.959 0.963 0.961 0.969 0.931 0.955 0.963 0.957 0.963 0.966 0.965 0.973 0.940 0.961 0.965 0.960 0.966 0.967 0.965 0.973 0.907 0.943 0.951 0.944 0.955 0.959 0.958 0.967

0.713 0.737 0.748 0.756 0.763 0.768 0.774 0.780 0.708 0.734 0.746 0.754 0.762 0.767 0.773 0.779 0.704 0.731 0.744 0.753 0.761 0.767 0.773 0.779 0.719 0.740 0.750 0.758 0.764 0.769 0.774 0.780

0.85 SB

PB BCPB

0.917 0.935 0.947 0.956 0.959 0.959 0.962 0.966 0.927 0.941 0.954 0.960 0.965 0.964 0.966 0.969 0.937 0.948 0.963 0.965 0.968 0.968 0.969 0.971 0.898 0.921 0.935 0.948 0.953 0.954 0.958 0.962

0.780 0.800 0.809 0.814 0.820 0.825 0.829 0.834 0.775 0.797 0.807 0.812 0.819 0.824 0.828 0.833 0.770 0.794 0.805 0.811 0.818 0.823 0.828 0.833 0.785 0.803 0.811 0.815 0.821 0.825 0.830 0.834

Table 26B. (continued)

T Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500 15.5 0.75 SB

PB BCPB

0.934 0.947 0.962 0.964 0.966 0.967 0.966 0.972 0.946 0.955 0.965 0.967 0.970 0.971 0.969 0.974 0.951 0.959 0.968 0.970 0.971 0.974 0.972 0.975 0.922 0.938 0.954 0.959 0.962 0.965 0.964 0.970

0.645 0.676 0.689 0.697 0.707 0.712 0.719 0.726 0.640 0.673 0.687 0.695 0.706 0.711 0.719 0.726 0.636 0.671 0.685 0.694 0.705 0.710 0.719 0.726 0.651 0.679 0.691 0.698 0.708 0.713 0.720 0.726

0.80 SB

PB BCPB

0.930 0.945 0.947 0.959 0.960 0.961 0.968 0.969 0.942 0.956 0.952 0.965 0.966 0.964 0.971 0.970 0.951 0.961 0.957 0.969 0.968 0.968 0.972 0.974 0.918 0.935 0.942 0.954 0.956 0.957 0.966 0.964

0.712 0.738 0.749 0.755 0.763 0.769 0.774 0.780 0.706 0.735 0.748 0.754 0.762 0.768 0.774 0.780 0.702 0.733 0.746 0.753 0.761 0.767 0.773 0.780 0.718 0.741 0.752 0.757 0.764 0.769 0.775 0.781

0.85 SB

PB BCPB

0.926 0.941 0.954 0.956 0.959 0.965 0.967 0.966 0.934 0.949 0.960 0.960 0.965 0.971 0.972 0.968 0.943 0.953 0.964 0.964 0.969 0.973 0.973 0.968 0.914 0.929 0.948 0.950 0.955 0.959 0.962 0.964

0.781 0.800 0.809 0.814 0.821 0.825 0.829 0.834 0.776 0.798 0.807 0.812 0.820 0.824 0.829 0.834 0.771 0.795 0.806 0.811 0.819 0.824 0.829 0.834 0.786 0.803 0.811 0.815 0.822 0.826 0.830 0.834

16 0.75 SB

PB BCPB

0.945 0.957 0.961 0.963 0.967 0.964 0.969 0.972 0.951 0.965 0.967 0.967 0.971 0.967 0.971 0.973 0.956 0.970 0.971 0.969 0.973 0.968 0.974 0.974 0.930 0.950 0.955 0.958 0.964 0.960 0.966 0.970

0.647 0.675 0.689 0.697 0.706 0.712 0.719 0.726 0.642 0.673 0.687 0.696 0.705 0.711 0.719 0.726 0.637 0.671 0.685 0.695 0.704 0.710 0.719 0.726 0.652 0.678 0.691 0.699 0.707 0.712 0.720 0.727

0.80 SB

PB BCPB0

0.928 0.954 0.957 0.961 0.965 0.964 0.968 0.968 0.938 0.960 0.962 0.967 0.969 0.967 0.971 0.971 0.946 0.967 0.966 0.971 0.971 0.971 0.971 0.972 0.913 0.941 0.949 0.950 0.959 0.959 0.964 0.966

0.716 0.737 0.749 0.756 0.764 0.769 0.774 0.780 0.711 0.734 0.747 0.755 0.763 0.768 0.774 0.780 0.706 0.732 0.745 0.754 0.762 0.768 0.774 0.780 0.721 0.740 0.751 0.758 0.765 0.770 0.775 0.781

0.85 SB

PB BCPB

0.923 0.942 0.950 0.956 0.958 0.963 0.963 0.970 0.934 0.952 0.957 0.961 0.962 0.966 0.965 0.974 0.943 0.957 0.963 0.968 0.967 0.968 0.968 0.975 0.909 0.929 0.937 0.950 0.953 0.959 0.959 0.967

0.783 0.802 0.811 0.815 0.821 0.825 0.830 0.834 0.779 0.799 0.809 0.814 0.820 0.824 0.830 0.834 0.774 0.797 0.808 0.813 0.819 0.824 0.829 0.834 0.789 0.804 0.813 0.817 0.822 0.826 0.831 0.835 14.5 0.75 SB

PB BCPB

0.943 0.951 0.954 0.957 0.962 0.967 0.966 0.973 0.951 0.959 0.961 0.962 0.966 0.969 0.968 0.974 0.957 0.964 0.964 0.964 0.968 0.971 0.970 0.977 0.925 0.940 0.948 0.952 0.957 0.964 0.964 0.971

0.643 0.674 0.687 0.697 0.706 0.711 0.718 0.725 0.637 0.671 0.685 0.695 0.705 0.710 0.718 0.725 0.633 0.669 0.683 0.694 0.704 0.710 0.717 0.725 0.649 0.678 0.689 0.698 0.707 0.712 0.719 0.726

0.80 SB

PB BCPB0

0.927 0.946 0.949 0.957 0.961 0.965 0.967 0.969 0.937 0.950 0.956 0.962 0.966 0.968 0.969 0.971 0.945 0.958 0.964 0.967 0.970 0.971 0.971 0.972 0.912 0.936 0.940 0.952 0.958 0.962 0.964 0.967

0.712 0.738 0.748 0.754 0.762 0.767 0.773 0.779 0.706 0.735 0.746 0.753 0.761 0.766 0.773 0.779 0.702 0.732 0.744 0.752 0.760 0.766 0.772 0.779 0.718 0.741 0.750 0.756 0.763 0.768 0.774 0.779

0.85 SB

PB BCPB

0.918 0.938 0.951 0.954 0.963 0.963 0.961 0.965 0.929 0.952 0.959 0.960 0.968 0.969 0.965 0.965 0.938 0.957 0.965 0.965 0.973 0.971 0.967 0.968 0.902 0.926 0.939 0.945 0.955 0.956 0.956 0.962

0.778 0.799 0.808 0.813 0.820 0.824 0.829 0.833 0.773 0.796 0.806 0.811 0.818 0.823 0.828 0.833 0.768 0.794 0.805 0.810 0.818 0.823 0.828 0.833 0.785 0.803 0.811 0.815 0.821 0.825 0.829 0.834

14 0.75 SB

PB BCPB

0.938 0.949 0.956 0.967 0.965 0.967 0.970 0.972 0.946 0.956 0.962 0.970 0.968 0.971 0.972 0.973 0.954 0.960 0.966 0.972 0.970 0.972 0.973 0.974 0.918 0.939 0.949 0.962 0.959 0.964 0.966 0.969

0.641 0.675 0.687 0.694 0.705 0.711 0.718 0.725 0.636 0.672 0.685 0.693 0.704 0.710 0.717 0.725 0.631 0.669 0.683 0.692 0.704 0.710 0.717 0.725 0.647 0.678 0.689 0.696 0.706 0.712 0.718 0.725

0.80 SB

PB BCPB0

0.925 0.948 0.954 0.958 0.963 0.965 0.966 0.971 0.936 0.957 0.960 0.962 0.968 0.969 0.969 0.973 0.947 0.961 0.964 0.965 0.970 0.971 0.971 0.975 0.904 0.938 0.949 0.951 0.959 0.962 0.964 0.968

0.713 0.735 0.747 0.755 0.762 0.768 0.773 0.779 0.708 0.732 0.745 0.753 0.761 0.767 0.773 0.779 0.703 0.730 0.743 0.752 0.760 0.766 0.772 0.778 0.719 0.739 0.749 0.756 0.763 0.769 0.774 0.779

0.85 SB

PB BCPB

0.920 0.940 0.944 0.956 0.958 0.960 0.963 0.966 0.930 0.951 0.950 0.965 0.963 0.965 0.968 0.969 0.939 0.958 0.956 0.970 0.968 0.968 0.970 0.971 0.901 0.927 0.931 0.949 0.952 0.952 0.957 0.963

0.777 0.798 0.807 0.813 0.819 0.823 0.828 0.833 0.771 0.795 0.805 0.811 0.817 0.822 0.828 0.833 0.766 0.793 0.803 0.810 0.816 0.822 0.827 0.832 0.783 0.802 0.810 0.815 0.820 0.824 0.829 0.833

Table 27A. Average bound and coverage percentage of 95% bootstrap for Chi-squared process with  ,0 k  .20

T Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

20 0.75 SB

PB BCPB

0.908 0.931 0.928 0.930 0.935 0.944 0.937 0.948 0.917 0.935 0.935 0.933 0.938 0.947 0.938 0.949 0.928 0.941 0.940 0.941 0.940 0.952 0.940 0.953 0.897 0.927 0.921 0.926 0.931 0.939 0.933 0.947

0.662 0.684 0.697 0.705 0.713 0.718 0.724 0.730 0.659 0.682 0.696 0.704 0.712 0.717 0.723 0.729 0.654 0.680 0.695 0.703 0.711 0.717 0.723 0.729 0.666 0.686 0.699 0.706 0.713 0.718 0.724 0.730

0.80 SB

PB BCPB

0.897 0.917 0.921 0.935 0.931 0.931 0.937 0.951 0.906 0.924 0.929 0.940 0.935 0.935 0.940 0.954 0.918 0.935 0.933 0.946 0.939 0.939 0.945 0.955 0.885 0.909 0.914 0.931 0.926 0.929 0.933 0.949

0.727 0.746 0.757 0.763 0.769 0.773 0.778 0.782 0.723 0.744 0.755 0.762 0.768 0.773 0.778 0.782 0.719 0.742 0.754 0.761 0.767 0.772 0.777 0.782 0.730 0.748 0.758 0.764 0.769 0.774 0.779 0.783

0.85 SB

PB BCPB

0.884 0.912 0.926 0.919 0.926 0.934 0.934 0.936 0.895 0.918 0.931 0.924 0.932 0.940 0.938 0.940 0.907 0.928 0.938 0.933 0.940 0.944 0.943 0.942 0.873 0.900 0.919 0.912 0.922 0.929 0.931 0.932

0.791 0.807 0.815 0.820 0.825 0.828 0.832 0.836 0.788 0.805 0.814 0.819 0.825 0.828 0.832 0.836 0.783 0.803 0.812 0.817 0.824 0.827 0.831 0.836 0.794 0.809 0.816 0.821 0.826 0.829 0.832 0.836 20.5 0.75 SB

PB BCPB

0.905 0.927 0.931 0.935 0.940 0.941 0.935 0.940 0.913 0.933 0.937 0.940 0.942 0.944 0.937 0.941 0.926 0.939 0.943 0.945 0.945 0.947 0.940 0.943 0.895 0.917 0.925 0.928 0.936 0.939 0.931 0.937

0.664 0.687 0.698 0.705 0.713 0.718 0.724 0.730 0.660 0.685 0.697 0.704 0.712 0.717 0.724 0.730 0.656 0.683 0.695 0.703 0.712 0.717 0.724 0.729 0.667 0.689 0.699 0.706 0.714 0.718 0.725 0.730

0.80 SB

PB BCPB

0.899 0.914 0.925 0.928 0.929 0.948 0.942 0.941 0.910 0.921 0.929 0.932 0.933 0.951 0.945 0.944 0.921 0.929 0.937 0.940 0.941 0.953 0.949 0.945 0.889 0.907 0.919 0.923 0.927 0.944 0.940 0.938

0.727 0.747 0.757 0.762 0.769 0.773 0.778 0.783 0.724 0.746 0.756 0.761 0.768 0.772 0.778 0.783 0.719 0.743 0.754 0.760 0.768 0.772 0.778 0.782 0.731 0.749 0.758 0.763 0.770 0.773 0.779 0.783

0.85 SB

PB BCPB

0.877 0.904 0.919 0.922 0.925 0.928 0.937 0.945 0.888 0.912 0.926 0.929 0.930 0.931 0.942 0.946 0.899 0.920 0.934 0.935 0.936 0.938 0.946 0.948 0.864 0.893 0.913 0.916 0.918 0.923 0.933 0.942

0.793 0.809 0.816 0.820 0.826 0.829 0.832 0.837 0.790 0.807 0.815 0.819 0.826 0.829 0.832 0.836 0.785 0.805 0.814 0.817 0.825 0.828 0.832 0.836 0.796 0.811 0.818 0.821 0.827 0.829 0.833 0.837

21 0.75 SB

PB BCPB

0.915 0.919 0.929 0.934 0.942 0.939 0.944 0.944 0.924 0.924 0.933 0.937 0.946 0.942 0.946 0.946 0.933 0.932 0.941 0.942 0.948 0.945 0.949 0.949 0.904 0.912 0.923 0.930 0.939 0.934 0.942 0.943

0.662 0.688 0.699 0.706 0.712 0.718 0.724 0.730 0.659 0.686 0.698 0.705 0.712 0.718 0.724 0.730 0.655 0.684 0.696 0.704 0.711 0.717 0.723 0.730 0.666 0.689 0.700 0.707 0.713 0.719 0.724 0.730

0.80 SB

PB BCPB0

0.908 0.921 0.925 0.925 0.928 0.94 0.943 0.944 0.918 0.927 0.932 0.932 0.932 0.943 0.945 0.948 0.931 0.934 0.939 0.938 0.938 0.947 0.947 0.950 0.900 0.911 0.918 0.920 0.925 0.936 0.941 0.943

0.726 0.747 0.757 0.763 0.77 0.773 0.778 0.783 0.723 0.745 0.756 0.762 0.769 0.773 0.778 0.783 0.719 0.743 0.754 0.760 0.768 0.772 0.778 0.783 0.730 0.749 0.758 0.763 0.770 0.774 0.779 0.784

0.85 SB

PB BCPB

0.877 0.903 0.922 0.916 0.936 0.927 0.947 0.937 0.889 0.914 0.930 0.926 0.940 0.931 0.949 0.940 0.899 0.922 0.937 0.932 0.945 0.937 0.953 0.943 0.866 0.891 0.915 0.909 0.929 0.923 0.943 0.934

0.793 0.810 0.816 0.821 0.826 0.829 0.832 0.837 0.790 0.808 0.815 0.820 0.825 0.829 0.832 0.837 0.786 0.806 0.813 0.819 0.824 0.828 0.832 0.836 0.796 0.811 0.817 0.822 0.826 0.830 0.833 0.837 19.5 0.75 SB

PB BCPB

0.903 0.903 0.927 0.937 0.935 0.939 0.943 0.943 0.915 0.913 0.932 0.940 0.937 0.941 0.944 0.946 0.927 0.922 0.938 0.945 0.943 0.947 0.948 0.948 0.891 0.897 0.921 0.933 0.931 0.936 0.94 0.941

0.660 0.687 0.697 0.704 0.712 0.717 0.723 0.729 0.657 0.685 0.696 0.703 0.711 0.717 0.723 0.729 0.652 0.683 0.694 0.702 0.710 0.716 0.722 0.729 0.664 0.689 0.698 0.705 0.712 0.718 0.723 0.729

0.80 SB

PB BCPB0

0.896 0.913 0.924 0.926 0.935 0.939 0.942 0.943 0.904 0.921 0.929 0.932 0.938 0.941 0.947 0.944 0.919 0.930 0.938 0.941 0.943 0.945 0.949 0.947 0.885 0.907 0.916 0.921 0.931 0.935 0.938 0.939

0.726 0.747 0.757 0.762 0.769 0.773 0.777 0.783 0.723 0.745 0.755 0.761 0.768 0.772 0.777 0.783 0.718 0.743 0.754 0.759 0.767 0.772 0.777 0.782 0.730 0.749 0.758 0.763 0.769 0.773 0.778 0.783

0.85 SB

PB BCPB

0.879 0.913 0.911 0.932 0.917 0.933 0.934 0.943 0.889 0.922 0.920 0.937 0.924 0.936 0.938 0.945 0.902 0.932 0.930 0.945 0.933 0.943 0.941 0.948 0.867 0.902 0.904 0.928 0.910 0.929 0.931 0.941

0.790 0.806 0.815 0.819 0.825 0.828 0.832 0.836 0.787 0.804 0.814 0.818 0.825 0.828 0.832 0.836 0.782 0.801 0.812 0.817 0.824 0.827 0.831 0.836 0.793 0.808 0.816 0.820 0.826 0.829 0.832 0.836

Table 27A. (continued)

19 0.75 SB

PB BCPB

0.900 0.914 0.931 0.933 0.945 0.946 0.941 0.944 0.910 0.922 0.938 0.939 0.948 0.949 0.945 0.946 0.924 0.931 0.944 0.944 0.951 0.953 0.949 0.948 0.889 0.904 0.925 0.928 0.941 0.942 0.939 0.941

0.661 0.687 0.696 0.704 0.713 0.717 0.723 0.729 0.658 0.685 0.695 0.703 0.712 0.716 0.723 0.729 0.653 0.682 0.694 0.702 0.711 0.716 0.722 0.729 0.665 0.688 0.698 0.705 0.713 0.717 0.723 0.729

0.80 SB

PB BCPB

0.899 0.922 0.930 0.939 0.929 0.936 0.938 0.932 0.909 0.928 0.935 0.943 0.936 0.939 0.943 0.937 0.924 0.934 0.943 0.948 0.942 0.942 0.946 0.940 0.886 0.914 0.922 0.932 0.925 0.930 0.935 0.929

0.724 0.746 0.756 0.761 0.768 0.773 0.778 0.783 0.721 0.744 0.755 0.760 0.768 0.772 0.777 0.783 0.716 0.741 0.753 0.759 0.767 0.772 0.777 0.782 0.728 0.748 0.757 0.762 0.769 0.773 0.778 0.783

0.85 SB

PB BCPB

0.891 0.906 0.908 0.930 0.931 0.932 0.933 0.939 0.904 0.916 0.915 0.935 0.935 0.937 0.935 0.941 0.914 0.926 0.926 0.941 0.943 0.941 0.938 0.944 0.880 0.900 0.900 0.924 0.924 0.927 0.929 0.936

0.788 0.806 0.815 0.818 0.824 0.827 0.832 0.836 0.784 0.804 0.814 0.817 0.823 0.827 0.831 0.836 0.780 0.802 0.812 0.816 0.822 0.826 0.831 0.835 0.792 0.808 0.817 0.819 0.825 0.828 0.832 0.836 Table 27B. Average bound and coverage percentage of 97.5% bootstrap for Chi-squared process with  ,0 k  .20

T Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

20 0.75 SB

PB BCPB

0.939 0.953 0.963 0.961 0.967 0.967 0.970 0.966 0.948 0.961 0.966 0.962 0.968 0.969 0.972 0.968 0.956 0.964 0.969 0.965 0.971 0.970 0.974 0.968 0.925 0.943 0.956 0.955 0.963 0.964 0.968 0.965

0.643 0.674 0.689 0.696 0.706 0.711 0.719 0.726 0.638 0.671 0.687 0.695 0.705 0.710 0.718 0.725 0.633 0.669 0.685 0.694 0.704 0.709 0.718 0.725 0.649 0.677 0.691 0.698 0.707 0.711 0.719 0.726

0.80 SB

PB BCPB

0.919 0.945 0.955 0.949 0.963 0.963 0.965 0.968 0.932 0.952 0.960 0.956 0.968 0.966 0.968 0.971 0.941 0.959 0.965 0.961 0.971 0.968 0.969 0.973 0.906 0.935 0.947 0.941 0.957 0.961 0.962 0.967

0.714 0.736 0.747 0.756 0.762 0.768 0.774 0.780 0.708 0.733 0.745 0.754 0.761 0.767 0.773 0.779 0.704 0.731 0.744 0.753 0.760 0.766 0.773 0.779 0.720 0.739 0.749 0.757 0.763 0.769 0.774 0.780

0.85 SB

PB BCPB

0.915 0.935 0.947 0.956 0.959 0.958 0.960 0.965 0.926 0.945 0.951 0.963 0.962 0.964 0.962 0.967 0.936 0.952 0.957 0.970 0.967 0.966 0.966 0.968 0.895 0.921 0.937 0.948 0.954 0.954 0.956 0.964

0.780 0.800 0.809 0.814 0.820 0.824 0.829 0.834 0.775 0.797 0.807 0.812 0.819 0.823 0.828 0.833 0.770 0.794 0.805 0.811 0.818 0.823 0.828 0.833 0.786 0.803 0.811 0.815 0.821 0.825 0.830 0.834 20.5 0.75 SB

PB BCPB

0.930 0.947 0.958 0.964 0.963 0.968 0.966 0.972 0.942 0.953 0.961 0.968 0.968 0.971 0.968 0.974 0.949 0.959 0.966 0.972 0.969 0.974 0.969 0.975 0.916 0.935 0.952 0.959 0.959 0.965 0.964 0.969

0.645 0.676 0.688 0.696 0.707 0.711 0.719 0.726 0.640 0.673 0.686 0.695 0.706 0.711 0.718 0.725 0.636 0.671 0.685 0.693 0.705 0.710 0.718 0.725 0.651 0.679 0.690 0.698 0.708 0.712 0.719 0.726

0.80 SB

PB BCPB0

0.934 0.953 0.957 0.957 0.962 0.961 0.963 0.972 0.942 0.962 0.964 0.962 0.967 0.964 0.967 0.973 0.948 0.966 0.968 0.965 0.971 0.967 0.970 0.975 0.917 0.942 0.948 0.953 0.958 0.956 0.960 0.969

0.711 0.736 0.749 0.755 0.763 0.768 0.774 0.780 0.706 0.733 0.747 0.753 0.762 0.768 0.773 0.780 0.701 0.731 0.745 0.752 0.761 0.767 0.773 0.779 0.717 0.739 0.751 0.757 0.764 0.769 0.774 0.780

0.85 SB

PB BCPB

0.920 0.947 0.947 0.959 0.958 0.962 0.969 0.966 0.933 0.955 0.953 0.964 0.964 0.967 0.970 0.968 0.941 0.960 0.958 0.969 0.968 0.970 0.971 0.970 0.902 0.933 0.940 0.955 0.955 0.956 0.965 0.962

0.781 0.799 0.809 0.814 0.820 0.825 0.829 0.834 0.776 0.797 0.807 0.812 0.819 0.824 0.829 0.834 0.771 0.794 0.805 0.811 0.819 0.823 0.828 0.833 0.787 0.803 0.811 0.815 0.822 0.825 0.830 0.834

21 0.75 SB

PB BCPB

0.934 0.954 0.959 0.962 0.968 0.969 0.966 0.975 0.946 0.961 0.965 0.966 0.971 0.973 0.968 0.976 0.952 0.966 0.968 0.970 0.974 0.976 0.968 0.978 0.921 0.946 0.953 0.959 0.965 0.967 0.964 0.973

0.645 0.675 0.688 0.696 0.706 0.711 0.719 0.726 0.640 0.672 0.686 0.695 0.705 0.710 0.719 0.726 0.635 0.670 0.685 0.694 0.704 0.710 0.718 0.725 0.651 0.678 0.690 0.698 0.707 0.712 0.720 0.726

0.80 SB

PB BCPB0

0.932 0.942 0.956 0.956 0.966 0.962 0.965 0.965 0.940 0.951 0.960 0.961 0.969 0.964 0.967 0.967 0.950 0.956 0.964 0.965 0.973 0.967 0.970 0.969 0.916 0.933 0.949 0.949 0.960 0.959 0.963 0.962

0.714 0.737 0.748 0.756 0.764 0.768 0.774 0.780 0.709 0.735 0.746 0.754 0.763 0.768 0.774 0.780 0.704 0.732 0.744 0.753 0.762 0.767 0.773 0.779 0.720 0.741 0.750 0.757 0.765 0.769 0.775 0.780

0.85 SB

PB BCPB

0.913 0.942 0.947 0.951 0.964 0.958 0.968 0.966 0.929 0.953 0.957 0.960 0.967 0.965 0.971 0.969 0.936 0.957 0.962 0.964 0.970 0.970 0.973 0.971 0.897 0.930 0.936 0.943 0.961 0.951 0.964 0.963

0.782 0.801 0.810 0.815 0.820 0.825 0.830 0.834 0.777 0.798 0.808 0.814 0.819 0.824 0.829 0.834 0.773 0.796 0.806 0.813 0.819 0.824 0.829 0.834 0.787 0.804 0.812 0.817 0.821 0.826 0.830 0.835

Table 27B. (continued) 19.5 0.75 SB

PB BCPB

0.946 0.947 0.958 0.957 0.966 0.963 0.972 0.971 0.955 0.955 0.964 0.963 0.968 0.966 0.975 0.972 0.962 0.962 0.968 0.965 0.971 0.967 0.976 0.972 0.933 0.938 0.951 0.950 0.960 0.961 0.970 0.970

0.638 0.674 0.686 0.696 0.705 0.711 0.718 0.725 0.633 0.671 0.684 0.694 0.704 0.710 0.718 0.725 0.628 0.668 0.683 0.693 0.704 0.710 0.717 0.725 0.645 0.677 0.688 0.697 0.706 0.712 0.719 0.726

0.80 SB

PB BCPB0

0.928 0.940 0.947 0.954 0.967 0.967 0.963 0.970 0.939 0.951 0.954 0.961 0.971 0.969 0.966 0.973 0.949 0.957 0.958 0.965 0.975 0.973 0.968 0.973 0.913 0.934 0.940 0.945 0.964 0.963 0.962 0.968

0.710 0.736 0.748 0.755 0.762 0.767 0.773 0.779 0.705 0.733 0.746 0.753 0.761 0.766 0.773 0.779 0.700 0.731 0.744 0.752 0.760 0.766 0.773 0.778 0.717 0.739 0.750 0.756 0.763 0.768 0.774 0.779

0.85 SB

PB BCPB

0.911 0.932 0.948 0.945 0.963 0.961 0.968 0.965 0.924 0.940 0.957 0.952 0.968 0.965 0.970 0.968 0.934 0.949 0.961 0.958 0.971 0.969 0.974 0.970 0.891 0.919 0.938 0.937 0.958 0.953 0.963 0.962

0.778 0.799 0.809 0.813 0.819 0.824 0.829 0.833 0.772 0.796 0.807 0.812 0.818 0.823 0.828 0.833 0.767 0.793 0.805 0.810 0.817 0.822 0.828 0.833 0.784 0.802 0.811 0.815 0.821 0.825 0.829 0.834

19 0.75 SB

PB BCPB

0.939 0.950 0.955 0.957 0.967 0.966 0.972 0.973 0.949 0.957 0.959 0.963 0.970 0.968 0.973 0.974 0.956 0.961 0.964 0.967 0.970 0.970 0.974 0.975 0.926 0.944 0.945 0.951 0.961 0.959 0.969 0.971

0.641 0.673 0.687 0.695 0.705 0.712 0.718 0.725 0.635 0.670 0.685 0.693 0.704 0.711 0.717 0.725 0.631 0.667 0.684 0.692 0.703 0.710 0.717 0.725 0.647 0.676 0.690 0.697 0.706 0.712 0.718 0.725

0.80 SB

PB BCPB0

0.930 0.946 0.956 0.958 0.956 0.965 0.966 0.972 0.939 0.953 0.965 0.965 0.961 0.968 0.968 0.975 0.949 0.958 0.969 0.968 0.966 0.971 0.970 0.977 0.912 0.934 0.947 0.951 0.951 0.959 0.961 0.971

0.711 0.736 0.747 0.755 0.762 0.768 0.774 0.779 0.705 0.733 0.745 0.753 0.761 0.767 0.773 0.779 0.701 0.731 0.743 0.752 0.760 0.766 0.773 0.778 0.717 0.739 0.749 0.756 0.763 0.768 0.774 0.779

0.85 SB

PB BCPB

0.911 0.933 0.940 0.946 0.963 0.959 0.965 0.964 0.923 0.944 0.951 0.956 0.970 0.965 0.966 0.967 0.934 0.953 0.956 0.960 0.974 0.967 0.967 0.969 0.893 0.922 0.931 0.937 0.955 0.955 0.962 0.962

0.778 0.797 0.808 0.813 0.819 0.823 0.828 0.833 0.773 0.794 0.806 0.812 0.818 0.823 0.828 0.833 0.768 0.792 0.804 0.810 0.817 0.822 0.827 0.832 0.785 0.801 0.810 0.815 0.820 0.824 0.829 0.833 Table 28A. Average bound and coverage percentage of 95% bootstrap for Gamma process with  ,12  ,2    / .

T Y_c bootstrap

(Coverage percentage) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

6 0.80 SB

PB BCPB

0.893 0.922 0.929 0.933 0.937 0.940 0.945 0.941 0.900 0.926 0.934 0.940 0.941 0.944 0.949 0.943 0.912 0.933 0.940 0.944 0.945 0.947 0.951 0.945 0.878 0.915 0.922 0.928 0.933 0.936 0.943 0.939

0.727 0.747 0.755 0.763 0.768 0.773 0.778 0.783 0.724 0.745 0.754 0.762 0.768 0.773 0.777 0.783 0.720 0.743 0.752 0.761 0.767 0.772 0.777 0.782 0.731 0.749 0.756 0.764 0.769 0.774 0.778 0.783

0.85 SB

PB BCPB

0.876 0.906 0.913 0.924 0.930 0.931 0.939 0.941 0.887 0.916 0.921 0.931 0.936 0.935 0.941 0.942 0.901 0.923 0.930 0.937 0.942 0.940 0.943 0.944 0.860 0.893 0.907 0.916 0.924 0.926 0.936 0.938

0.792 0.808 0.815 0.820 0.825 0.829 0.832 0.836 0.789 0.806 0.813 0.819 0.824 0.828 0.832 0.836 0.784 0.803 0.812 0.817 0.824 0.827 0.831 0.836 0.795 0.81 0.816 0.821 0.826 0.829 0.832 0.836

0.90 SB

PB BCPB

0.859 0.887 0.906 0.915 0.920 0.923 0.925 0.927 0.868 0.895 0.916 0.923 0.926 0.930 0.931 0.932 0.884 0.909 0.929 0.932 0.934 0.936 0.935 0.938 0.846 0.877 0.895 0.907 0.910 0.916 0.919 0.923

0.859 0.869 0.875 0.878 0.882 0.884 0.887 0.890 0.856 0.868 0.874 0.877 0.881 0.884 0.887 0.890 0.852 0.865 0.872 0.876 0.881 0.883 0.886 0.890 0.862 0.871 0.876 0.879 0.883 0.885 0.888 0.890

6.5 0.80 SB

PB BCPB

0.894 0.921 0.930 0.928 0.933 0.938 0.945 0.945 0.903 0.927 0.934 0.932 0.938 0.942 0.947 0.946 0.914 0.936 0.940 0.937 0.943 0.944 0.951 0.949 0.886 0.911 0.922 0.922 0.928 0.934 0.943 0.942

0.728 0.748 0.757 0.763 0.769 0.774 0.778 0.783 0.725 0.746 0.756 0.762 0.769 0.773 0.778 0.783 0.721 0.744 0.755 0.761 0.768 0.773 0.777 0.783 0.732 0.750 0.758 0.764 0.770 0.774 0.778 0.784

0.85 SB

PB BCPB0

0.881 0.911 0.919 0.925 0.931 0.931 0.935 0.941 0.888 0.921 0.927 0.932 0.935 0.934 0.940 0.942 0.902 0.928 0.937 0.940 0.942 0.940 0.946 0.944 0.865 0.901 0.913 0.918 0.926 0.928 0.932 0.938

0.794 0.783 0.783 0.783 0.783 0.829 0.833 0.837 0.791 0.778 0.778 0.778 0.778 0.829 0.833 0.837 0.787 0.774 0.774 0.774 0.774 0.828 0.833 0.836 0.797 0.788 0.788 0.788 0.788 0.830 0.833 0.837

0.90 SB

PB BCPB

0.869 0.898 0.909 0.925 0.926 0.933 0.934 0.939 0.882 0.903 0.917 0.931 0.931 0.940 0.938 0.942 0.895 0.917 0.928 0.938 0.936 0.945 0.943 0.945 0.854 0.888 0.902 0.919 0.921 0.925 0.928 0.936

0.862 0.872 0.876 0.880 0.883 0.885 0.888 0.891 0.860 0.871 0.875 0.879 0.883 0.885 0.888 0.891 0.856 0.869 0.874 0.878 0.882 0.884 0.888 0.891 0.864 0.874 0.877 0.88 0.884 0.886 0.888 0.891

Table 28A. (continued)

7 0.80 SB

PB BCPB

0.899 0.920 0.927 0.929 0.924 0.940 0.939 0.940 0.910 0.928 0.934 0.933 0.929 0.943 0.941 0.943 0.921 0.937 0.940 0.941 0.936 0.947 0.947 0.945 0.889 0.913 0.921 0.926 0.922 0.935 0.938 0.938

0.730 0.749 0.758 0.764 0.771 0.774 0.779 0.784 0.727 0.748 0.757 0.763 0.770 0.774 0.778 0.784 0.723 0.745 0.756 0.762 0.770 0.773 0.778 0.784 0.733 0.751 0.759 0.765 0.772 0.775 0.779 0.784

0.85 SB

PB BCPB

0.887 0.918 0.923 0.926 0.930 0.936 0.937 0.940 0.899 0.926 0.929 0.932 0.933 0.937 0.939 0.941 0.914 0.935 0.936 0.939 0.940 0.941 0.942 0.946 0.876 0.911 0.917 0.920 0.926 0.930 0.932 0.939

0.797 0.811 0.818 0.822 0.827 0.830 0.834 0.838 0.794 0.809 0.817 0.821 0.827 0.830 0.834 0.837 0.791 0.807 0.815 0.820 0.826 0.829 0.833 0.837 0.800 0.812 0.819 0.823 0.828 0.831 0.834 0.838

0.90 SB

PB BCPB

0.885 0.909 0.912 0.926 0.929 0.938 0.938 0.935 0.892 0.920 0.919 0.932 0.931 0.942 0.942 0.936 0.904 0.928 0.926 0.937 0.935 0.946 0.945 0.941 0.877 0.901 0.905 0.922 0.923 0.932 0.938 0.931

0.864 0.874 0.878 0.881 0.884 0.887 0.889 0.892 0.862 0.873 0.878 0.881 0.884 0.886 0.889 0.892 0.860 0.871 0.877 0.880 0.883 0.886 0.888 0.891 0.866 0.875 0.879 0.882 0.885 0.887 0.889 0.892

5.5 0.80 SB

PB BCPB

0.892 0.913 0.924 0.931 0.931 0.939 0.947 0.952 0.902 0.923 0.930 0.934 0.936 0.943 0.951 0.954 0.916 0.932 0.942 0.943 0.941 0.946 0.953 0.959 0.877 0.907 0.918 0.925 0.923 0.934 0.944 0.948

0.723 0.746 0.755 0.760 0.769 0.772 0.777 0.782 0.720 0.744 0.754 0.759 0.768 0.771 0.777 0.782 0.715 0.741 0.752 0.758 0.767 0.771 0.776 0.782 0.727 0.748 0.757 0.761 0.769 0.772 0.777 0.782

0.85 SB

PB BCPB0

0.877 0.901 0.914 0.924 0.929 0.934 0.938 0.942 0.886 0.913 0.921 0.927 0.935 0.941 0.940 0.945 0.898 0.927 0.932 0.934 0.944 0.947 0.945 0.947 0.864 0.892 0.904 0.918 0.923 0.927 0.935 0.940

0.789 0.806 0.813 0.818 0.824 0.827 0.831 0.836 0.785 0.804 0.812 0.817 0.823 0.827 0.831 0.835 0.780 0.801 0.810 0.816 0.822 0.826 0.831 0.835 0.793 0.808 0.815 0.819 0.824 0.828 0.832 0.836

0.90 SB

PB BCPB

0.852 0.878 0.903 0.913 0.925 0.927 0.924 0.936 0.865 0.887 0.914 0.920 0.930 0.931 0.931 0.940 0.875 0.904 0.925 0.929 0.940 0.937 0.937 0.944 0.835 0.866 0.889 0.901 0.918 0.923 0.917 0.932

0.854 0.867 0.872 0.876 0.880 0.883 0.886 0.889 0.851 0.865 0.871 0.875 0.879 0.882 0.886 0.889 0.846 0.862 0.869 0.874 0.878 0.881 0.885 0.889 0.858 0.869 0.874 0.878 0.881 0.883 0.886 0.889

5 0.75 SB

PB BCPB

0.905 0.916 0.930 0.929 0.942 0.938 0.936 0.942 0.914 0.922 0.936 0.935 0.946 0.941 0.939 0.945 0.925 0.929 0.944 0.939 0.949 0.944 0.942 0.947 0.895 0.906 0.922 0.924 0.938 0.934 0.932 0.940

0.657 0.683 0.694 0.703 0.710 0.716 0.722 0.728 0.653 0.681 0.693 0.702 0.709 0.715 0.722 0.728 0.648 0.678 0.691 0.701 0.708 0.715 0.721 0.727 0.661 0.685 0.695 0.704 0.710 0.716 0.722 0.728

0.80 SB

PB BCPB0

0.891 0.908 0.927 0.928 0.939 0.941 0.941 0.937 0.903 0.920 0.935 0.936 0.943 0.944 0.945 0.939 0.916 0.929 0.943 0.943 0.946 0.947 0.948 0.944 0.877 0.901 0.919 0.924 0.935 0.936 0.939 0.933

0.723 0.745 0.754 0.760 0.767 0.771 0.776 0.782 0.720 0.743 0.752 0.758 0.766 0.770 0.776 0.782 0.714 0.740 0.751 0.757 0.765 0.770 0.775 0.781 0.727 0.747 0.755 0.761 0.768 0.771 0.776 0.782

0.85 SB

PB BCPB

0.878 0.903 0.923 0.928 0.931 0.938 0.933 0.934 0.891 0.910 0.931 0.932 0.935 0.943 0.938 0.937 0.908 0.925 0.939 0.943 0.939 0.948 0.943 0.939 0.864 0.892 0.915 0.919 0.923 0.933 0.929 0.930

0.786 0.804 0.812 0.817 0.823 0.826 0.831 0.835 0.783 0.802 0.810 0.816 0.822 0.826 0.830 0.835 0.777 0.799 0.808 0.814 0.821 0.825 0.830 0.835 0.790 0.806 0.813 0.818 0.823 0.827 0.831 0.835 Table 28B. Average bound and coverage percentage of 97.5% bootstrap for Gamma process with  ,12  ,2    / .

T Y_c bootstrap

(Coverage percentage ) Samples Size( n) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

6 0.80 SB

PB BCPB

0.929 0.947 0.953 0.958 0.960 0.964 0.966 0.969 0.942 0.953 0.958 0.965 0.967 0.966 0.968 0.970 0.949 0.957 0.962 0.968 0.972 0.969 0.970 0.972 0.912 0.938 0.948 0.950 0.954 0.960 0.963 0.967

0.713 0.736 0.748 0.754 0.763 0.768 0.774 0.779 0.707 0.733 0.746 0.753 0.762 0.767 0.773 0.779 0.702 0.731 0.744 0.751 0.761 0.766 0.773 0.779 0.719 0.740 0.750 0.756 0.764 0.769 0.774 0.780

0.85 SB

PB BCPB

0.918 0.937 0.950 0.950 0.960 0.962 0.965 0.967 0.931 0.946 0.958 0.958 0.965 0.967 0.968 0.969 0.936 0.951 0.962 0.960 0.968 0.970 0.970 0.971 0.896 0.923 0.939 0.941 0.954 0.957 0.961 0.965

0.780 0.800 0.809 0.814 0.820 0.824 0.829 0.833 0.775 0.797 0.807 0.812 0.819 0.823 0.828 0.833 0.770 0.794 0.805 0.811 0.818 0.822 0.828 0.833 0.786 0.803 0.811 0.815 0.821 0.825 0.829 0.834

0.90 SB

PB BCPB

0.893 0.916 0.940 0.938 0.940 0.951 0.963 0.967 0.908 0.930 0.946 0.945 0.950 0.955 0.968 0.969 0.919 0.938 0.951 0.952 0.956 0.960 0.971 0.972 0.872 0.906 0.928 0.929 0.932 0.944 0.957 0.963

0.851 0.863 0.869 0.874 0.879 0.882 0.885 0.888 0.847 0.860 0.867 0.873 0.878 0.881 0.884 0.888 0.842 0.858 0.866 0.871 0.877 0.880 0.884 0.887 0.856 0.866 0.871 0.876 0.880 0.882 0.885 0.888

Table 28B. (continued)

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

6.5 0.80 SB

PB BCPB

0.929 0.947 0.952 0.963 0.963 0.964 0.966 0.970 0.941 0.954 0.961 0.967 0.968 0.968 0.970 0.973 0.948 0.961 0.965 0.970 0.971 0.970 0.972 0.974 0.915 0.935 0.948 0.955 0.959 0.959 0.961 0.967

0.714 0.739 0.749 0.755 0.764 0.769 0.775 0.780 0.709 0.736 0.747 0.754 0.763 0.768 0.774 0.780 0.705 0.734 0.746 0.753 0.762 0.768 0.774 0.779 0.720 0.742 0.751 0.757 0.765 0.770 0.775 0.780

0.85 SB

PB BCPB

0.921 0.940 0.949 0.954 0.958 0.965 0.965 0.967 0.933 0.950 0.956 0.962 0.963 0.968 0.968 0.969 0.939 0.954 0.962 0.964 0.967 0.971 0.970 0.971 0.904 0.932 0.941 0.946 0.953 0.960 0.961 0.964

0.783 0.801 0.811 0.815 0.821 0.825 0.83 0.834 0.778 0.799 0.809 0.814 0.820 0.825 0.829 0.834 0.774 0.797 0.807 0.812 0.819 0.824 0.829 0.834 0.788 0.804 0.813 0.817 0.822 0.826 0.830 0.835

0.90 SB

PB BCPB

0.904 0.936 0.945 0.945 0.952 0.955 0.961 0.967 0.919 0.943 0.954 0.950 0.959 0.962 0.966 0.969 0.928 0.949 0.959 0.956 0.963 0.965 0.968 0.974 0.888 0.926 0.934 0.937 0.947 0.951 0.957 0.962

0.854 0.866 0.872 0.876 0.880 0.883 0.886 0.889 0.850 0.864 0.870 0.874 0.879 0.882 0.885 0.889 0.847 0.862 0.869 0.873 0.879 0.881 0.885 0.888 0.858 0.869 0.874 0.877 0.881 0.883 0.886 0.889

7 0.80 SB

PB BCPB

0.934 0.953 0.959 0.961 0.963 0.962 0.968 0.971 0.946 0.962 0.963 0.967 0.967 0.965 0.971 0.973 0.952 0.967 0.968 0.969 0.971 0.968 0.973 0.974 0.922 0.944 0.951 0.956 0.960 0.956 0.966 0.969

0.716 0.740 0.751 0.757 0.765 0.770 0.775 0.781 0.711 0.737 0.749 0.756 0.764 0.769 0.775 0.780 0.707 0.735 0.747 0.755 0.764 0.769 0.774 0.780 0.721 0.742 0.753 0.758 0.766 0.771 0.776 0.781

0.85 SB

PB BCPB0

0.926 0.948 0.955 0.961 0.962 0.968 0.967 0.970 0.937 0.954 0.961 0.966 0.967 0.970 0.971 0.971 0.945 0.957 0.967 0.968 0.969 0.972 0.973 0.972 0.916 0.938 0.950 0.955 0.958 0.966 0.963 0.967

0.785 0.804 0.812 0.817 0.823 0.826 0.831 0.835 0.781 0.802 0.810 0.816 0.822 0.826 0.830 0.835 0.777 0.800 0.809 0.815 0.821 0.825 0.830 0.835 0.789 0.807 0.814 0.818 0.824 0.827 0.831 0.835

0.90 SB

PB BCPB

0.915 0.941 0.952 0.954 0.959 0.961 0.963 0.965 0.924 0.947 0.957 0.959 0.963 0.963 0.966 0.967 0.936 0.952 0.962 0.963 0.968 0.966 0.969 0.969 0.898 0.930 0.942 0.947 0.953 0.957 0.956 0.961

0.857 0.869 0.875 0.877 0.882 0.884 0.887 0.890 0.854 0.867 0.873 0.876 0.881 0.884 0.887 0.890 0.851 0.866 0.872 0.876 0.880 0.883 0.886 0.889 0.860 0.871 0.876 0.878 0.882 0.885 0.887 0.890

5.5 0.80 SB

PB BCPB

0.925 0.946 0.953 0.957 0.960 0.963 0.966 0.967 0.939 0.956 0.961 0.963 0.965 0.966 0.969 0.969 0.944 0.962 0.965 0.966 0.968 0.968 0.972 0.969 0.909 0.934 0.946 0.947 0.956 0.957 0.963 0.966

0.709 0.736 0.767 0.779 0.762 0.767 0.773 0.779 0.703 0.733 0.766 0.779 0.761 0.766 0.772 0.779 0.698 0.730 0.765 0.778 0.760 0.765 0.772 0.778 0.715 0.739 0.768 0.779 0.763 0.768 0.773 0.779

0.85 SB

PB BCPB0

0.909 0.931 0.946 0.948 0.956 0.962 0.961 0.964 0.920 0.943 0.954 0.956 0.961 0.966 0.965 0.967 0.926 0.951 0.961 0.962 0.967 0.970 0.967 0.969 0.892 0.920 0.938 0.939 0.950 0.957 0.957 0.962

0.776 0.798 0.806 0.812 0.819 0.823 0.828 0.833 0.770 0.795 0.804 0.810 0.818 0.822 0.827 0.833 0.765 0.792 0.802 0.809 0.817 0.821 0.827 0.832 0.783 0.801 0.809 0.814 0.820 0.824 0.829 0.833

0.90 SB

PB BCPB

0.884 0.913 0.927 0.946 0.951 0.959 0.956 0.960 0.898 0.927 0.938 0.953 0.958 0.964 0.960 0.963 0.910 0.937 0.953 0.960 0.961 0.969 0.967 0.967 0.863 0.896 0.907 0.935 0.943 0.954 0.948 0.956

0.845 0.861 0.868 0.872 0.877 0.879 0.883 0.887 0.840 0.857 0.865 0.870 0.875 0.878 0.883 0.887 0.835 0.855 0.864 0.868 0.874 0.878 0.882 0.886 0.852 0.864 0.870 0.873 0.878 0.880 0.884 0.887

5 0.75 SB

PB BCPB

0.929 0.952 0.954 0.960 0.961 0.964 0.971 0.969 0.939 0.956 0.961 0.968 0.965 0.967 0.974 0.969 0.947 0.960 0.967 0.969 0.968 0.969 0.976 0.970 0.914 0.941 0.946 0.954 0.955 0.960 0.968 0.966

0.638 0.671 0.685 0.693 0.703 0.708 0.716 0.724 0.632 0.668 0.683 0.691 0.702 0.708 0.716 0.724 0.627 0.665 0.681 0.690 0.701 0.707 0.715 0.723 0.645 0.675 0.688 0.695 0.705 0.709 0.717 0.724

0.80 SB

PB BCPB0

0.917 0.942 0.955 0.953 0.956 0.964 0.968 0.968 0.929 0.949 0.960 0.960 0.961 0.969 0.970 0.972 0.939 0.953 0.965 0.965 0.962 0.973 0.974 0.974 0.900 0.929 0.943 0.950 0.950 0.963 0.964 0.965

0.708 0.734 0.745 0.752 0.761 0.766 0.772 0.778 0.702 0.731 0.742 0.750 0.759 0.765 0.772 0.778 0.696 0.728 0.741 0.749 0.758 0.764 0.771 0.778 0.715 0.738 0.747 0.754 0.762 0.767 0.773 0.779

0.85 SB

PB BCPB

0.911 0.934 0.946 0.950 0.957 0.957 0.964 0.971 0.924 0.949 0.951 0.956 0.960 0.962 0.967 0.973 0.933 0.957 0.957 0.962 0.962 0.965 0.971 0.975 0.890 0.920 0.931 0.940 0.951 0.952 0.959 0.967

0.775 0.795 0.805 0.811 0.818 0.822 0.827 0.832 0.769 0.792 0.802 0.809 0.817 0.821 0.826 0.831 0.763 0.789 0.800 0.808 0.816 0.820 0.826 0.831 0.782 0.799 0.807 0.813 0.819 0.823 0.828 0.832

Table 29A. Average bound and coverage percentage of 95% bootstrap for Gamma process with  ,15  ,2    / .

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

7.5 0.80 SB

PB BCPB

0.895 0.914 0.924 0.933 0.934 0.934 0.943 0.942 0.906 0.921 0.928 0.937 0.939 0.938 0.946 0.944 0.920 0.930 0.936 0.942 0.942 0.942 0.950 0.947 0.884 0.904 0.917 0.928 0.929 0.930 0.940 0.941

0.727 0.747 0.756 0.762 0.769 0.773 0.778 0.783 0.724 0.745 0.755 0.761 0.768 0.773 0.777 0.783 0.719 0.742 0.753 0.760 0.768 0.772 0.777 0.782 0.731 0.749 0.758 0.763 0.770 0.774 0.778 0.783

0.85 SB

PB BCPB

0.879 0.902 0.915 0.926 0.930 0.933 0.940 0.937 0.890 0.911 0.923 0.932 0.934 0.936 0.942 0.940 0.907 0.924 0.933 0.940 0.941 0.940 0.946 0.943 0.862 0.892 0.907 0.918 0.926 0.928 0.935 0.934

0.792 0.807 0.816 0.819 0.825 0.828 0.832 0.836 0.789 0.805 0.814 0.818 0.824 0.828 0.832 0.836 0.784 0.803 0.813 0.817 0.823 0.827 0.831 0.836 0.795 0.809 0.817 0.820 0.826 0.829 0.832 0.836

0.90 SB

PB BCPB

0.870 0.887 0.904 0.909 0.920 0.929 0.935 0.936 0.881 0.897 0.913 0.918 0.926 0.933 0.939 0.939 0.895 0.912 0.928 0.925 0.934 0.941 0.944 0.942 0.856 0.875 0.891 0.900 0.912 0.922 0.929 0.933

0.858 0.87 0.875 0.878 0.882 0.884 0.887 0.890 0.855 0.868 0.874 0.877 0.881 0.884 0.887 0.890 0.851 0.866 0.873 0.876 0.880 0.883 0.886 0.890 0.861 0.871 0.876 0.879 0.882 0.885 0.887 0.890

8 0.80 SB

PB BCPB

0.901 0.913 0.931 0.928 0.928 0.936 0.936 0.938 0.910 0.918 0.935 0.933 0.932 0.938 0.939 0.940 0.921 0.931 0.941 0.938 0.937 0.943 0.943 0.941 0.891 0.906 0.925 0.921 0.925 0.933 0.931 0.936

0.726 0.748 0.757 0.763 0.769 0.773 0.778 0.783 0.723 0.746 0.755 0.762 0.769 0.773 0.778 0.783 0.719 0.744 0.754 0.761 0.768 0.772 0.778 0.783 0.730 0.750 0.758 0.764 0.770 0.774 0.779 0.784

0.85 SB

PB BCPB0

0.891 0.913 0.921 0.925 0.930 0.933 0.935 0.939 0.898 0.923 0.928 0.929 0.935 0.937 0.936 0.941 0.911 0.933 0.939 0.936 0.941 0.942 0.940 0.944 0.873 0.905 0.911 0.919 0.926 0.928 0.931 0.937

0.793 0.808 0.816 0.820 0.826 0.829 0.833 0.837 0.790 0.807 0.815 0.820 0.825 0.828 0.832 0.836 0.786 0.804 0.813 0.818 0.825 0.828 0.832 0.836 0.797 0.810 0.817 0.821 0.827 0.829 0.833 0.837

0.90 SB

PB BCPB

0.875 0.897 0.911 0.924 0.927 0.934 0.930 0.935 0.888 0.907 0.920 0.928 0.931 0.939 0.933 0.937 0.901 0.919 0.928 0.933 0.939 0.945 0.938 0.939 0.861 0.885 0.904 0.917 0.919 0.928 0.925 0.932

0.860 0.872 0.876 0.879 0.883 0.885 0.888 0.891 0.857 0.870 0.876 0.878 0.882 0.885 0.888 0.891 0.854 0.868 0.874 0.877 0.882 0.884 0.887 0.890 0.862 0.873 0.877 0.880 0.883 0.885 0.888 0.891

8.5 0.80 SB

PB BCPB

0.911 0.921 0.927 0.926 0.930 0.936 0.944 0.943 0.920 0.926 0.934 0.932 0.935 0.940 0.946 0.946 0.931 0.935 0.938 0.938 0.941 0.945 0.949 0.950 0.897 0.911 0.919 0.921 0.927 0.931 0.942 0.940

0.728 0.749 0.759 0.765 0.770 0.774 0.779 0.784 0.725 0.748 0.757 0.764 0.770 0.773 0.779 0.783 0.721 0.745 0.756 0.763 0.769 0.773 0.778 0.783 0.731 0.751 0.760 0.765 0.771 0.774 0.779 0.784

0.85 SB

PB BCPB0

0.893 0.918 0.929 0.929 0.924 0.934 0.937 0.941 0.903 0.924 0.934 0.936 0.931 0.937 0.941 0.942 0.916 0.932 0.940 0.940 0.937 0.943 0.945 0.946 0.879 0.912 0.921 0.923 0.918 0.929 0.932 0.937

0.797 0.81 0.817 0.821 0.827 0.830 0.833 0.837 0.794 0.808 0.816 0.820 0.827 0.829 0.833 0.837 0.790 0.806 0.815 0.819 0.826 0.829 0.833 0.837 0.799 0.811 0.818 0.822 0.828 0.830 0.834 0.838

0.90 SB

PB BCPB

0.883 0.902 0.920 0.925 0.925 0.928 0.934 0.941 0.891 0.912 0.926 0.932 0.929 0.933 0.938 0.944 0.905 0.923 0.934 0.940 0.935 0.940 0.940 0.947 0.870 0.893 0.909 0.919 0.922 0.925 0.931 0.937

0.863 0.872 0.878 0.881 0.884 0.887 0.889 0.891 0.861 0.871 0.877 0.880 0.883 0.886 0.888 0.891 0.858 0.870 0.876 0.879 0.883 0.886 0.888 0.891 0.865 0.874 0.879 0.881 0.884 0.887 0.889 0.891

7 0.80 SB

PB BCPB

0.900 0.917 0.922 0.921 0.925 0.935 0.941 0.946 0.913 0.927 0.929 0.926 0.928 0.939 0.945 0.947 0.925 0.940 0.935 0.934 0.935 0.942 0.949 0.951 0.888 0.913 0.916 0.915 0.920 0.932 0.938 0.944

0.724 0.745 0.755 0.761 0.769 0.772 0.777 0.782 0.720 0.743 0.754 0.760 0.768 0.772 0.777 0.782 0.716 0.741 0.752 0.759 0.767 0.771 0.776 0.782 0.728 0.747 0.757 0.762 0.770 0.773 0.778 0.782

0.85 SB

PB BCPB0

0.877 0.907 0.919 0.920 0.924 0.928 0.936 0.943 0.890 0.915 0.925 0.927 0.929 0.933 0.940 0.944 0.906 0.926 0.932 0.931 0.934 0.940 0.945 0.947 0.865 0.895 0.910 0.915 0.920 0.926 0.933 0.940

0.790 0.807 0.814 0.818 0.824 0.828 0.831 0.836 0.787 0.805 0.812 0.817 0.823 0.827 0.831 0.835 0.782 0.802 0.810 0.816 0.822 0.827 0.831 0.835 0.794 0.809 0.815 0.819 0.825 0.828 0.832 0.836

0.90 SB

PB BCPB

0.858 0.878 0.898 0.908 0.914 0.923 0.930 0.935 0.872 0.888 0.906 0.918 0.919 0.931 0.935 0.939 0.888 0.904 0.918 0.929 0.929 0.937 0.939 0.944 0.841 0.867 0.885 0.901 0.906 0.916 0.923 0.932

0.855 0.868 0.873 0.877 0.881 0.883 0.886 0.889 0.852 0.866 0.872 0.876 0.880 0.883 0.886 0.889 0.847 0.864 0.870 0.874 0.879 0.882 0.885 0.889 0.859 0.870 0.874 0.878 0.882 0.884 0.887 0.890

Table 29A. (continued)

6.5 0.75 SB

PB BCPB

0.905 0.927 0.932 0.934 0.935 0.943 0.940 0.940 0.912 0.933 0.937 0.940 0.941 0.944 0.941 0.942 0.923 0.940 0.942 0.948 0.945 0.947 0.945 0.945 0.894 0.922 0.924 0.928 0.931 0.939 0.937 0.938

0.655 0.681 0.694 0.702 0.711 0.716 0.723 0.728 0.652 0.679 0.693 0.701 0.710 0.716 0.722 0.728 0.647 0.677 0.691 0.699 0.709 0.715 0.722 0.728 0.659 0.683 0.695 0.703 0.711 0.717 0.723 0.728

0.80 SB

PB BCPB

0.896 0.918 0.924 0.928 0.936 0.932 0.939 0.938 0.905 0.925 0.930 0.932 0.940 0.936 0.940 0.940 0.919 0.936 0.938 0.941 0.945 0.939 0.945 0.942 0.881 0.902 0.915 0.922 0.932 0.929 0.936 0.935

0.723 0.745 0.754 0.760 0.767 0.771 0.777 0.782 0.719 0.743 0.753 0.759 0.766 0.771 0.776 0.782 0.714 0.740 0.751 0.758 0.765 0.770 0.776 0.782 0.727 0.747 0.756 0.761 0.767 0.772 0.777 0.783

0.85 SB

PB BCPB

0.874 0.910 0.914 0.926 0.929 0.932 0.934 0.939 0.884 0.920 0.922 0.931 0.934 0.936 0.938 0.942 0.899 0.931 0.931 0.937 0.940 0.941 0.943 0.945 0.855 0.896 0.904 0.919 0.922 0.927 0.929 0.936

0.788 0.803 0.813 0.817 0.823 0.827 0.831 0.835 0.784 0.801 0.811 0.816 0.822 0.826 0.830 0.835 0.779 0.798 0.809 0.815 0.821 0.825 0.830 0.835 0.792 0.806 0.814 0.818 0.824 0.827 0.831 0.835 Table 29B. Average bound and coverage percentage of 97.5% bootstrap for Gamma process with  ,15  ,2    / .

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

7.5 0.80 SB

PB BCPB

0.924 0.942 0.952 0.957 0.964 0.965 0.967 0.972 0.935 0.949 0.956 0.963 0.969 0.969 0.969 0.973 0.945 0.954 0.960 0.966 0.972 0.972 0.972 0.973 0.913 0.934 0.947 0.949 0.961 0.961 0.964 0.969

0.711 0.737 0.747 0.754 0.763 0.767 0.774 0.780 0.705 0.734 0.745 0.752 0.762 0.767 0.773 0.780 0.701 0.731 0.744 0.751 0.761 0.766 0.773 0.779 0.717 0.740 0.749 0.756 0.764 0.768 0.774 0.780

0.85 SB

PB BCPB

0.919 0.935 0.947 0.954 0.958 0.959 0.965 0.970 0.931 0.947 0.954 0.959 0.965 0.963 0.968 0.971 0.939 0.952 0.959 0.962 0.967 0.968 0.971 0.973 0.902 0.922 0.938 0.945 0.954 0.953 0.960 0.968

0.780 0.799 0.808 0.813 0.820 0.824 0.829 0.833 0.775 0.796 0.806 0.812 0.819 0.823 0.829 0.833 0.770 0.794 0.804 0.811 0.818 0.823 0.828 0.833 0.786 0.802 0.810 0.815 0.821 0.825 0.830 0.833

0.90 SB

PB BCPB

0.896 0.919 0.939 0.946 0.951 0.956 0.961 0.963 0.911 0.930 0.949 0.952 0.957 0.962 0.965 0.966 0.922 0.938 0.957 0.957 0.961 0.964 0.969 0.969 0.879 0.909 0.927 0.937 0.945 0.951 0.955 0.959

0.849 0.864 0.870 0.874 0.878 0.881 0.885 0.888 0.844 0.861 0.868 0.872 0.877 0.880 0.884 0.888 0.840 0.859 0.866 0.871 0.876 0.880 0.884 0.887 0.854 0.867 0.872 0.875 0.879 0.882 0.885 0.888

8 0.80 SB

PB BCPB

0.935 0.945 0.947 0.958 0.961 0.964 0.963 0.970 0.946 0.952 0.954 0.964 0.963 0.968 0.965 0.971 0.951 0.960 0.962 0.967 0.966 0.970 0.968 0.972 0.921 0.933 0.938 0.951 0.956 0.957 0.959 0.969

0.714 0.738 0.739 0.750 0.763 0.768 0.774 0.780 0.709 0.736 0.736 0.748 0.762 0.768 0.774 0.780 0.704 0.733 0.734 0.746 0.762 0.767 0.774 0.779 0.720 0.742 0.742 0.752 0.764 0.769 0.775 0.780

0.85 SB

PB BCPB0

0.919 0.942 0.946 0.955 0.956 0.960 0.968 0.969 0.930 0.954 0.953 0.961 0.964 0.964 0.971 0.972 0.937 0.960 0.958 0.967 0.967 0.968 0.973 0.973 0.902 0.932 0.935 0.950 0.951 0.957 0.964 0.966

0.782 0.800 0.810 0.815 0.821 0.825 0.829 0.834 0.777 0.797 0.808 0.813 0.820 0.824 0.829 0.834 0.772 0.795 0.806 0.812 0.820 0.824 0.828 0.833 0.787 0.803 0.812 0.816 0.822 0.826 0.830 0.834

0.90 SB

PB BCPB

0.906 0.937 0.949 0.947 0.951 0.956 0.962 0.964 0.920 0.947 0.953 0.956 0.956 0.963 0.966 0.967 0.931 0.951 0.961 0.960 0.960 0.966 0.969 0.968 0.891 0.928 0.939 0.942 0.946 0.949 0.957 0.960

0.852 0.865 0.871 0.875 0.880 0.883 0.886 0.889 0.849 0.863 0.870 0.873 0.879 0.882 0.885 0.889 0.845 0.861 0.868 0.872 0.879 0.881 0.885 0.888 0.857 0.868 0.873 0.876 0.881 0.883 0.886 0.889

8.5 0.80 SB

PB BCPB

0.927 0.952 0.956 0.959 0.966 0.968 0.965 0.969 0.938 0.961 0.962 0.966 0.969 0.971 0.966 0.971 0.947 0.968 0.967 0.969 0.972 0.972 0.968 0.973 0.911 0.943 0.951 0.955 0.961 0.966 0.962 0.966

0.717 0.738 0.750 0.756 0.764 0.769 0.775 0.780 0.712 0.736 0.748 0.755 0.763 0.768 0.774 0.780 0.708 0.734 0.746 0.754 0.763 0.768 0.774 0.780 0.723 0.741 0.752 0.758 0.765 0.770 0.775 0.781

0.85 SB

PB BCPB0

0.920 0.939 0.951 0.952 0.959 0.968 0.964 0.966 0.930 0.949 0.955 0.956 0.965 0.971 0.967 0.969 0.937 0.955 0.958 0.961 0.969 0.972 0.968 0.970 0.906 0.929 0.942 0.944 0.955 0.963 0.959 0.963

0.785 0.803 0.811 0.816 0.822 0.826 0.831 0.835 0.781 0.800 0.810 0.815 0.821 0.825 0.830 0.834 0.777 0.798 0.808 0.814 0.820 0.825 0.830 0.834 0.790 0.806 0.813 0.818 0.823 0.827 0.831 0.835

0.90 SB

PB BCPB

0.920 0.936 0.947 0.954 0.959 0.961 0.962 0.965 0.931 0.948 0.952 0.962 0.965 0.964 0.966 0.970 0.942 0.954 0.958 0.964 0.969 0.968 0.968 0.969 0.907 0.925 0.938 0.946 0.954 0.956 0.958 0.961

0.855 0.868 0.873 0.876 0.881 0.884 0.887 0.890 0.852 0.866 0.872 0.875 0.880 0.883 0.886 0.890 0.849 0.864 0.871 0.875 0.880 0.883 0.886 0.889 0.859 0.870 0.875 0.877 0.882 0.884 0.887 0.890

Table 29B. (continued)

7 0.80 SB

PB BCPB

0.930 0.948 0.951 0.956 0.959 0.963 0.964 0.968 0.938 0.955 0.957 0.961 0.964 0.968 0.966 0.971 0.946 0.963 0.962 0.965 0.968 0.970 0.969 0.971 0.915 0.938 0.941 0.949 0.954 0.959 0.959 0.966

0.708 0.734 0.747 0.754 0.762 0.767 0.773 0.779 0.702 0.731 0.744 0.752 0.761 0.766 0.773 0.778 0.697 0.728 0.743 0.751 0.760 0.765 0.772 0.778 0.714 0.737 0.749 0.756 0.763 0.768 0.774 0.779

0.85 SB

PB BCPB

0.909 0.937 0.948 0.953 0.958 0.962 0.964 0.965 0.923 0.946 0.956 0.960 0.961 0.966 0.968 0.966 0.932 0.952 0.960 0.963 0.965 0.969 0.969 0.968 0.893 0.922 0.937 0.942 0.953 0.957 0.961 0.959

0.778 0.798 0.807 0.812 0.819 0.823 0.828 0.833 0.773 0.794 0.804 0.810 0.818 0.822 0.827 0.833 0.768 0.792 0.802 0.809 0.817 0.822 0.827 0.832 0.785 0.801 0.809 0.814 0.820 0.824 0.829 0.833

0.90 SB

PB BCPB

0.884 0.915 0.934 0.937 0.948 0.954 0.958 0.963 0.899 0.926 0.944 0.945 0.954 0.961 0.964 0.965 0.908 0.935 0.950 0.954 0.960 0.966 0.968 0.967 0.863 0.898 0.919 0.926 0.938 0.948 0.953 0.959

0.847 0.861 0.867 0.873 0.877 0.880 0.884 0.887 0.842 0.858 0.865 0.871 0.876 0.879 0.883 0.887 0.837 0.855 0.863 0.870 0.875 0.878 0.883 0.887 0.853 0.864 0.870 0.874 0.878 0.881 0.884 0.888

6.5 0.75 SB

PB BCPB

0.931 0.946 0.956 0.960 0.965 0.964 0.967 0.969 0.943 0.952 0.962 0.965 0.970 0.967 0.970 0.970 0.952 0.960 0.967 0.968 0.971 0.971 0.971 0.970 0.915 0.937 0.948 0.956 0.961 0.961 0.964 0.967

0.638 0.671 0.685 0.693 0.704 0.709 0.717 0.724 0.632 0.668 0.683 0.691 0.702 0.708 0.716 0.724 0.627 0.665 0.681 0.690 0.702 0.707 0.716 0.724 0.645 0.674 0.687 0.695 0.705 0.710 0.718 0.725

0.80 SB

PB BCPB0

0.919 0.940 0.954 0.958 0.959 0.966 0.965 0.970 0.930 0.948 0.958 0.964 0.962 0.969 0.967 0.972 0.937 0.957 0.964 0.967 0.966 0.972 0.971 0.974 0.904 0.929 0.948 0.952 0.953 0.962 0.963 0.967

0.707 0.734 0.745 0.753 0.761 0.766 0.773 0.778 0.702 0.731 0.743 0.751 0.760 0.765 0.772 0.778 0.696 0.728 0.741 0.750 0.759 0.765 0.772 0.778 0.714 0.738 0.747 0.755 0.763 0.767 0.773 0.779

0.85 SB

PB BCPB

0.912 0.935 0.950 0.953 0.958 0.960 0.962 0.967 0.925 0.945 0.958 0.961 0.965 0.962 0.966 0.970 0.935 0.952 0.961 0.964 0.970 0.965 0.968 0.972 0.897 0.920 0.937 0.941 0.950 0.951 0.957 0.963

0.775 0.796 0.805 0.811 0.818 0.822 0.828 0.832 0.769 0.793 0.802 0.809 0.817 0.821 0.827 0.832 0.764 0.790 0.800 0.808 0.816 0.820 0.827 0.831 0.783 0.800 0.807 0.813 0.819 0.823 0.828 0.832 Table 30A. Average bound and coverage percentage of 95% bootstrap for Gamma process with  ,20  ,2    / .

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

10 0.80 SB

PB BCPB

0.904 0.920 0.926 0.929 0.932 0.938 0.941 0.945 0.912 0.924 0.930 0.935 0.936 0.945 0.943 0.945 0.924 0.933 0.941 0.941 0.940 0.949 0.948 0.949 0.890 0.911 0.920 0.923 0.927 0.933 0.939 0.940

0.726 0.745 0.756 0.762 0.769 0.773 0.778 0.783 0.723 0.744 0.755 0.761 0.768 0.773 0.777 0.783 0.718 0.741 0.753 0.760 0.767 0.772 0.777 0.782 0.729 0.747 0.758 0.763 0.769 0.774 0.778 0.783

0.85 SB

PB BCPB

0.886 0.908 0.912 0.919 0.930 0.931 0.937 0.945 0.893 0.916 0.922 0.927 0.936 0.935 0.940 0.948 0.904 0.928 0.927 0.935 0.942 0.941 0.943 0.951 0.868 0.897 0.903 0.911 0.924 0.927 0.935 0.941

0.791 0.807 0.815 0.819 0.825 0.828 0.832 0.836 0.787 0.805 0.813 0.818 0.824 0.828 0.832 0.836 0.783 0.803 0.812 0.817 0.823 0.827 0.831 0.835 0.794 0.809 0.816 0.820 0.825 0.829 0.832 0.836

0.90 SB

PB BCPB

0.862 0.897 0.907 0.917 0.925 0.930 0.928 0.939 0.873 0.909 0.915 0.925 0.931 0.935 0.935 0.944 0.886 0.920 0.923 0.933 0.938 0.940 0.940 0.947 0.845 0.883 0.897 0.908 0.919 0.925 0.923 0.936

0.857 0.869 0.875 0.878 0.882 0.884 0.887 0.890 0.855 0.867 0.874 0.877 0.881 0.884 0.887 0.890 0.851 0.865 0.872 0.876 0.880 0.883 0.886 0.890 0.860 0.871 0.876 0.879 0.882 0.885 0.887 0.890 10.5 0.80 SB

PB BCPB

0.895 0.917 0.924 0.927 0.935 0.938 0.937 0.938 0.905 0.925 0.930 0.932 0.940 0.943 0.941 0.939 0.918 0.936 0.937 0.939 0.944 0.945 0.944 0.942 0.879 0.908 0.916 0.922 0.931 0.936 0.935 0.935

0.730 0.747 0.757 0.763 0.769 0.773 0.778 0.783 0.727 0.745 0.755 0.762 0.768 0.773 0.778 0.783 0.722 0.743 0.754 0.761 0.768 0.772 0.777 0.783 0.734 0.749 0.758 0.764 0.770 0.774 0.778 0.783

0.85 SB

PB BCPB0

0.892 0.911 0.922 0.929 0.928 0.932 0.938 0.938 0.902 0.918 0.928 0.932 0.934 0.936 0.939 0.942 0.912 0.924 0.935 0.939 0.939 0.939 0.943 0.947 0.879 0.904 0.913 0.921 0.923 0.927 0.934 0.933

0.791 0.808 0.816 0.820 0.826 0.829 0.833 0.836 0.788 0.806 0.815 0.819 0.825 0.828 0.832 0.836 0.783 0.804 0.813 0.818 0.824 0.828 0.832 0.836 0.794 0.809 0.817 0.821 0.826 0.829 0.833 0.836

0.90 SB

PB BCPB

0.884 0.905 0.911 0.926 0.923 0.931 0.932 0.939 0.891 0.912 0.918 0.932 0.927 0.937 0.937 0.943 0.903 0.920 0.925 0.938 0.938 0.941 0.942 0.947 0.868 0.895 0.902 0.917 0.915 0.925 0.927 0.935

0.859 0.871 0.876 0.879 0.883 0.885 0.888 0.890 0.856 0.869 0.875 0.878 0.883 0.885 0.888 0.890 0.853 0.867 0.874 0.877 0.882 0.884 0.887 0.890 0.862 0.872 0.877 0.879 0.884 0.886 0.888 0.891

Table 30A. (continued)

11 0.80 SB

PB BCPB

0.912 0.916 0.923 0.928 0.931 0.938 0.942 0.945 0.919 0.924 0.929 0.936 0.936 0.942 0.945 0.948 0.930 0.932 0.937 0.944 0.940 0.945 0.947 0.950 0.900 0.905 0.918 0.922 0.928 0.932 0.939 0.943

0.727 0.749 0.758 0.763 0.770 0.774 0.778 0.783 0.724 0.747 0.756 0.763 0.769 0.774 0.778 0.783 0.719 0.745 0.755 0.761 0.768 0.773 0.778 0.783 0.730 0.751 0.759 0.764 0.770 0.774 0.779 0.783

0.85 SB

PB BCPB

0.892 0.914 0.922 0.923 0.929 0.934 0.938 0.937 0.903 0.922 0.927 0.928 0.934 0.938 0.939 0.939 0.913 0.929 0.936 0.934 0.940 0.942 0.944 0.941 0.884 0.902 0.915 0.914 0.923 0.929 0.934 0.934

0.792 0.809 0.817 0.821 0.826 0.829 0.833 0.837 0.789 0.808 0.816 0.820 0.826 0.829 0.833 0.837 0.785 0.805 0.814 0.819 0.825 0.828 0.832 0.837 0.795 0.811 0.818 0.822 0.827 0.830 0.833 0.837

0.90 SB

PB BCPB

0.882 0.904 0.921 0.922 0.927 0.936 0.932 0.936 0.892 0.911 0.927 0.931 0.932 0.939 0.936 0.938 0.903 0.923 0.936 0.939 0.940 0.944 0.939 0.941 0.871 0.893 0.914 0.917 0.921 0.932 0.929 0.932

0.861 0.872 0.877 0.880 0.884 0.886 0.889 0.891 0.859 0.871 0.876 0.879 0.883 0.885 0.888 0.891 0.856 0.869 0.875 0.879 0.883 0.885 0.888 0.891 0.863 0.874 0.878 0.881 0.884 0.886 0.889 0.891

9.5 0.80 SB

PB BCPB

0.899 0.917 0.923 0.928 0.935 0.937 0.942 0.945 0.907 0.923 0.928 0.933 0.940 0.941 0.944 0.948 0.917 0.932 0.936 0.938 0.944 0.945 0.947 0.949 0.885 0.909 0.915 0.922 0.931 0.936 0.940 0.943

0.725 0.746 0.755 0.761 0.768 0.772 0.777 0.782 0.721 0.744 0.754 0.760 0.768 0.771 0.777 0.782 0.717 0.741 0.752 0.759 0.767 0.771 0.777 0.782 0.729 0.748 0.757 0.762 0.769 0.773 0.778 0.782

0.85 SB

PB BCPB0

0.882 0.901 0.910 0.914 0.927 0.932 0.938 0.941 0.892 0.912 0.917 0.923 0.933 0.936 0.940 0.942 0.905 0.921 0.925 0.934 0.939 0.942 0.943 0.946 0.868 0.887 0.903 0.903 0.920 0.925 0.934 0.938

0.788 0.807 0.814 0.819 0.824 0.828 0.831 0.836 0.785 0.805 0.813 0.818 0.823 0.828 0.831 0.836 0.780 0.802 0.811 0.817 0.823 0.827 0.831 0.835 0.792 0.809 0.816 0.820 0.825 0.829 0.832 0.836

0.90 SB

PB BCPB

0.863 0.891 0.906 0.915 0.925 0.930 0.932 0.939 0.876 0.905 0.913 0.920 0.931 0.938 0.938 0.941 0.890 0.916 0.921 0.928 0.936 0.943 0.943 0.944 0.850 0.879 0.898 0.906 0.917 0.923 0.927 0.936

0.855 0.868 0.873 0.877 0.881 0.883 0.886 0.889 0.853 0.866 0.872 0.876 0.880 0.883 0.886 0.889 0.848 0.864 0.870 0.875 0.879 0.882 0.885 0.889 0.859 0.870 0.875 0.878 0.881 0.884 0.887 0.889

9 0.75 SB

PB BCPB

0.905 0.921 0.928 0.931 0.938 0.939 0.935 0.941 0.915 0.926 0.932 0.938 0.941 0.942 0.936 0.943 0.928 0.937 0.941 0.945 0.949 0.945 0.940 0.946 0.894 0.915 0.923 0.927 0.933 0.937 0.932 0.938

0.656 0.684 0.695 0.702 0.711 0.717 0.723 0.729 0.653 0.682 0.694 0.701 0.710 0.716 0.722 0.729 0.648 0.679 0.692 0.699 0.710 0.716 0.722 0.729 0.660 0.686 0.697 0.703 0.712 0.717 0.723 0.729

0.80 SB

PB BCPB0

0.895 0.920 0.926 0.931 0.932 0.932 0.933 0.937 0.909 0.926 0.934 0.937 0.938 0.936 0.935 0.939 0.921 0.938 0.942 0.943 0.941 0.942 0.940 0.943 0.884 0.907 0.918 0.923 0.928 0.926 0.928 0.934

0.723 0.745 0.755 0.761 0.768 0.772 0.778 0.783 0.719 0.743 0.753 0.760 0.767 0.772 0.777 0.782 0.714 0.740 0.752 0.758 0.766 0.771 0.777 0.782 0.726 0.747 0.756 0.762 0.769 0.773 0.778 0.783

0.85 SB

PB BCPB

0.888 0.913 0.925 0.924 0.922 0.927 0.931 0.937 0.897 0.923 0.933 0.932 0.928 0.932 0.934 0.939 0.912 0.932 0.940 0.938 0.935 0.939 0.939 0.942 0.871 0.900 0.916 0.917 0.917 0.920 0.926 0.934

0.787 0.803 0.813 0.817 0.823 0.827 0.831 0.836 0.783 0.801 0.811 0.816 0.823 0.827 0.831 0.835 0.778 0.799 0.810 0.815 0.822 0.826 0.830 0.835 0.791 0.806 0.814 0.819 0.824 0.828 0.831 0.836 Table 30B. Average bound and coverage percentage of 97.5% bootstrap for Gamma process with  ,20  ,2    / .

T Y_c bootstrap

(Coverage percentage ) Samples Size( n) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

10 0.80 SB

PB BCPB

0.931 0.945 0.952 0.955 0.961 0.965 0.965 0.968 0.941 0.951 0.959 0.960 0.963 0.969 0.967 0.969 0.950 0.957 0.964 0.962 0.965 0.970 0.968 0.970 0.918 0.933 0.944 0.949 0.957 0.960 0.961 0.966

0.710 0.737 0.748 0.754 0.763 0.767 0.774 0.780 0.704 0.734 0.746 0.752 0.762 0.766 0.773 0.779 0.699 0.732 0.745 0.751 0.761 0.766 0.773 0.779 0.716 0.740 0.751 0.755 0.764 0.768 0.774 0.780

0.85 SB

PB BCPB

0.912 0.938 0.951 0.955 0.961 0.965 0.963 0.970 0.925 0.949 0.959 0.961 0.967 0.969 0.967 0.971 0.933 0.956 0.966 0.966 0.971 0.972 0.970 0.974 0.896 0.928 0.939 0.946 0.954 0.958 0.959 0.967

0.781 0.798 0.807 0.814 0.819 0.824 0.829 0.833 0.775 0.795 0.805 0.812 0.818 0.823 0.828 0.833 0.771 0.793 0.804 0.811 0.817 0.823 0.828 0.833 0.787 0.802 0.810 0.816 0.820 0.825 0.830 0.834

0.90 SB

PB BCPB

0.902 0.926 0.936 0.945 0.953 0.956 0.959 0.964 0.914 0.939 0.947 0.953 0.958 0.961 0.965 0.966 0.922 0.948 0.951 0.959 0.963 0.966 0.967 0.969 0.885 0.911 0.924 0.936 0.943 0.948 0.952 0.960

0.849 0.864 0.870 0.873 0.878 0.881 0.885 0.888 0.845 0.861 0.868 0.872 0.877 0.880 0.884 0.888 0.840 0.859 0.866 0.871 0.876 0.880 0.884 0.888 0.854 0.867 0.872 0.875 0.879 0.882 0.885 0.888

Table 30B. (continued)

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500 10.5 0.80 SB

PB BCPB

0.925 0.942 0.955 0.956 0.962 0.966 0.965 0.971 0.933 0.951 0.964 0.961 0.966 0.970 0.968 0.973 0.941 0.958 0.969 0.965 0.968 0.973 0.970 0.974 0.903 0.930 0.945 0.950 0.958 0.961 0.962 0.970

0.715 0.738 0.749 0.756 0.763 0.768 0.774 0.780 0.710 0.735 0.747 0.754 0.762 0.767 0.774 0.779 0.705 0.733 0.745 0.753 0.762 0.767 0.773 0.779 0.721 0.741 0.751 0.757 0.765 0.769 0.775 0.780

0.85 SB

PB BCPB

0.922 0.938 0.950 0.955 0.957 0.959 0.965 0.970 0.935 0.948 0.957 0.960 0.962 0.964 0.969 0.972 0.942 0.955 0.962 0.963 0.966 0.968 0.971 0.973 0.905 0.928 0.938 0.947 0.952 0.954 0.960 0.969

0.781 0.799 0.809 0.814 0.821 0.825 0.829 0.834 0.776 0.797 0.807 0.813 0.820 0.824 0.829 0.834 0.772 0.794 0.806 0.812 0.819 0.824 0.828 0.833 0.787 0.803 0.811 0.816 0.822 0.826 0.830 0.834

0.90 SB

PB BCPB

0.911 0.936 0.946 0.953 0.960 0.957 0.961 0.967 0.922 0.944 0.954 0.958 0.965 0.963 0.965 0.969 0.932 0.953 0.961 0.965 0.968 0.965 0.969 0.971 0.896 0.923 0.935 0.947 0.954 0.952 0.957 0.963

0.851 0.865 0.871 0.874 0.879 0.882 0.885 0.889 0.847 0.862 0.869 0.873 0.878 0.881 0.885 0.888 0.843 0.860 0.868 0.872 0.877 0.881 0.885 0.888 0.856 0.867 0.873 0.875 0.880 0.883 0.886 0.889

11 0.80 SB

PB BCPB

0.934 0.951 0.954 0.957 0.963 0.962 0.966 0.972 0.947 0.957 0.961 0.961 0.969 0.967 0.968 0.973 0.954 0.962 0.967 0.966 0.971 0.970 0.971 0.974 0.918 0.941 0.948 0.949 0.957 0.957 0.964 0.970

0.714 0.738 0.749 0.756 0.764 0.769 0.775 0.780 0.709 0.735 0.747 0.754 0.763 0.768 0.774 0.780 0.704 0.733 0.745 0.753 0.762 0.768 0.774 0.780 0.720 0.741 0.751 0.757 0.765 0.770 0.775 0.780

0.85 SB

PB BCPB0

0.920 0.939 0.950 0.958 0.959 0.961 0.961 0.970 0.935 0.946 0.960 0.963 0.964 0.967 0.964 0.971 0.941 0.954 0.966 0.966 0.970 0.969 0.964 0.973 0.901 0.928 0.940 0.949 0.956 0.956 0.955 0.967

0.783 0.801 0.810 0.815 0.822 0.826 0.830 0.834 0.778 0.799 0.809 0.813 0.821 0.825 0.829 0.834 0.774 0.796 0.807 0.812 0.820 0.824 0.829 0.834 0.788 0.804 0.812 0.816 0.823 0.826 0.830 0.834

0.90 SB

PB BCPB

0.909 0.938 0.941 0.954 0.954 0.960 0.958 0.973 0.923 0.945 0.948 0.960 0.960 0.964 0.960 0.975 0.933 0.953 0.953 0.965 0.964 0.967 0.963 0.977 0.896 0.925 0.928 0.945 0.946 0.952 0.955 0.969

0.854 0.867 0.873 0.876 0.880 0.883 0.886 0.889 0.851 0.865 0.871 0.875 0.880 0.882 0.886 0.889 0.848 0.863 0.870 0.874 0.879 0.882 0.885 0.889 0.858 0.869 0.874 0.877 0.881 0.883 0.887 0.889

9.5 0.80 SB

PB BCPB

0.936 0.948 0.952 0.955 0.963 0.961 0.965 0.968 0.945 0.956 0.959 0.961 0.967 0.966 0.967 0.972 0.954 0.962 0.964 0.964 0.968 0.968 0.969 0.975 0.924 0.935 0.945 0.948 0.957 0.955 0.962 0.966

0.708 0.735 0.747 0.754 0.762 0.767 0.773 0.779 0.702 0.732 0.745 0.752 0.760 0.766 0.772 0.778 0.697 0.730 0.743 0.751 0.760 0.766 0.772 0.778 0.714 0.739 0.749 0.756 0.763 0.768 0.774 0.779

0.85 SB

PB BCPB0

0.915 0.937 0.945 0.953 0.958 0.961 0.964 0.967 0.925 0.947 0.955 0.961 0.963 0.966 0.969 0.969 0.934 0.955 0.961 0.965 0.966 0.970 0.970 0.971 0.897 0.923 0.932 0.942 0.952 0.956 0.961 0.964

0.776 0.798 0.807 0.812 0.819 0.823 0.828 0.833 0.771 0.794 0.805 0.811 0.818 0.822 0.827 0.833 0.766 0.792 0.803 0.809 0.817 0.822 0.827 0.832 0.782 0.801 0.809 0.814 0.820 0.824 0.829 0.833

0.90 SB

PB BCPB

0.891 0.930 0.937 0.944 0.956 0.956 0.960 0.962 0.904 0.942 0.944 0.952 0.962 0.962 0.964 0.965 0.915 0.948 0.955 0.959 0.966 0.967 0.967 0.966 0.870 0.913 0.921 0.936 0.948 0.949 0.955 0.960

0.848 0.861 0.868 0.872 0.877 0.880 0.884 0.887 0.843 0.858 0.866 0.871 0.876 0.879 0.883 0.887 0.838 0.855 0.864 0.869 0.875 0.879 0.883 0.887 0.854 0.864 0.870 0.874 0.878 0.881 0.884 0.888

9 0.75 SB

PB BCPB

0.938 0.952 0.958 0.957 0.962 0.965 0.967 0.972 0.947 0.960 0.963 0.961 0.965 0.967 0.970 0.974 0.955 0.964 0.967 0.966 0.968 0.969 0.972 0.974 0.919 0.943 0.949 0.949 0.957 0.962 0.966 0.970

0.637 0.670 0.685 0.694 0.703 0.710 0.717 0.725 0.632 0.667 0.683 0.692 0.702 0.709 0.717 0.724 0.627 0.665 0.682 0.691 0.701 0.708 0.716 0.724 0.644 0.674 0.688 0.695 0.704 0.711 0.718 0.725

0.80 SB

PB BCPB0

0.924 0.945 0.957 0.960 0.965 0.963 0.965 0.968 0.935 0.950 0.964 0.965 0.970 0.966 0.967 0.969 0.944 0.958 0.967 0.970 0.973 0.968 0.970 0.970 0.911 0.934 0.949 0.953 0.960 0.957 0.959 0.964

0.708 0.735 0.746 0.753 0.761 0.766 0.773 0.779 0.702 0.731 0.744 0.751 0.760 0.766 0.773 0.778 0.697 0.729 0.742 0.750 0.759 0.765 0.772 0.778 0.715 0.738 0.748 0.755 0.763 0.767 0.774 0.779

0.85 SB

PB BCPB

0.911 0.934 0.949 0.958 0.963 0.962 0.963 0.968 0.923 0.942 0.958 0.966 0.969 0.965 0.967 0.971 0.933 0.951 0.965 0.972 0.971 0.970 0.969 0.974 0.895 0.921 0.939 0.950 0.957 0.954 0.959 0.964

0.774 0.796 0.806 0.811 0.819 0.822 0.828 0.833 0.768 0.793 0.804 0.809 0.817 0.821 0.827 0.832 0.762 0.790 0.802 0.808 0.816 0.821 0.826 0.832 0.780 0.800 0.808 0.813 0.820 0.823 0.828 0.833

Table 31A. Average bound and coverage percentage of 95% bootstrap for Weibull process with  ,10 3.6,



¹ ¹



   ^ .

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

 0.80 SB PB BCPB

0.903 0.913 0.927 0.934 0.934 0.935 0.937 0.942 0.912 0.923 0.934 0.937 0.939 0.939 0.940 0.944 0.921 0.931 0.942 0.942 0.945 0.943 0.944 0.945 0.888 0.905 0.920 0.930 0.931 0.933 0.933 0.940

0.725 0.747 0.756 0.762 0.768 0.773 0.778 0.783 0.722 0.745 0.754 0.761 0.768 0.772 0.778 0.782 0.717 0.743 0.753 0.760 0.767 0.772 0.778 0.782 0.729 0.749 0.757 0.763 0.769 0.773 0.779 0.783

0.85 SB

PB BCPB

0.889 0.911 0.925 0.925 0.931 0.934 0.937 0.935 0.899 0.922 0.933 0.930 0.938 0.937 0.939 0.939 0.910 0.937 0.939 0.938 0.945 0.943 0.945 0.944 0.877 0.902 0.917 0.916 0.926 0.929 0.934 0.933

0.791 0.808 0.814 0.820 0.825 0.829 0.832 0.836 0.787 0.806 0.813 0.819 0.825 0.828 0.832 0.836 0.783 0.804 0.812 0.817 0.824 0.828 0.831 0.836 0.794 0.810 0.816 0.821 0.826 0.829 0.832 0.836

0.90 SB

PB BCPB

0.873 0.903 0.911 0.921 0.923 0.930 0.933 0.934 0.883 0.911 0.917 0.927 0.928 0.936 0.936 0.939 0.897 0.923 0.926 0.933 0.936 0.941 0.942 0.942 0.864 0.891 0.905 0.916 0.917 0.927 0.927 0.932

0.860 0.870 0.876 0.879 0.883 0.885 0.888 0.890 0.858 0.869 0.875 0.878 0.882 0.885 0.888 0.890 0.854 0.867 0.873 0.877 0.881 0.884 0.887 0.890 0.862 0.872 0.877 0.880 0.883 0.885 0.888 0.891

0.5 0.80 SB PB BCPB

0.901 0.919 0.924 0.933 0.933 0.938 0.941 0.938 0.911 0.928 0.929 0.938 0.937 0.941 0.943 0.940 0.923 0.937 0.935 0.944 0.942 0.944 0.946 0.942 0.889 0.910 0.917 0.927 0.927 0.936 0.938 0.936

0.724 0.746 0.757 0.762 0.769 0.772 0.778 0.783 0.721 0.745 0.756 0.761 0.768 0.772 0.777 0.783 0.716 0.742 0.754 0.759 0.767 0.771 0.777 0.782 0.728 0.748 0.758 0.763 0.769 0.773 0.778 0.783

0.85 SB

PB BCPB0

0.890 0.919 0.920 0.922 0.929 0.935 0.940 0.938 0.900 0.927 0.929 0.928 0.935 0.940 0.943 0.941 0.912 0.936 0.936 0.935 0.940 0.946 0.946 0.944 0.876 0.912 0.912 0.916 0.924 0.930 0.936 0.936

0.791 0.806 0.815 0.820 0.825 0.828 0.832 0.836 0.788 0.804 0.814 0.819 0.825 0.828 0.832 0.836 0.783 0.801 0.812 0.818 0.824 0.827 0.831 0.836 0.794 0.808 0.816 0.821 0.826 0.829 0.833 0.836

0.90 SB

PB BCPB

0.875 0.904 0.912 0.919 0.925 0.939 0.940 0.943 0.884 0.914 0.919 0.924 0.930 0.941 0.943 0.946 0.898 0.926 0.930 0.932 0.936 0.946 0.946 0.948 0.863 0.895 0.903 0.911 0.919 0.934 0.937 0.938

0.86 0.871 0.875 0.879 0.883 0.885 0.887 0.890 0.858 0.869 0.875 0.878 0.882 0.884 0.887 0.890 0.854 0.867 0.873 0.877 0.881 0.884 0.887 0.890 0.863 0.872 0.877 0.880 0.883 0.885 0.888 0.890

 0.801 SB PB BCPB

0.904 0.916 0.926 0.932 0.938 0.944 0.936 0.944 0.912 0.925 0.931 0.937 0.941 0.947 0.941 0.946 0.925 0.933 0.938 0.942 0.946 0.952 0.943 0.948 0.895 0.905 0.920 0.928 0.934 0.940 0.932 0.941

0.724 0.746 0.756 0.761 0.768 0.772 0.778 0.783 0.721 0.744 0.755 0.761 0.768 0.772 0.777 0.783 0.716 0.741 0.753 0.759 0.767 0.771 0.777 0.782 0.728 0.748 0.757 0.762 0.769 0.773 0.778 0.783

0.85 SB

PB BCPB0

0.879 0.905 0.922 0.928 0.930 0.932 0.938 0.941 0.889 0.914 0.929 0.935 0.934 0.934 0.943 0.943 0.905 0.924 0.935 0.942 0.940 0.939 0.946 0.946 0.864 0.893 0.911 0.921 0.923 0.927 0.934 0.939

0.791 0.808 0.814 0.819 0.825 0.828 0.832 0.836 0.788 0.806 0.813 0.818 0.824 0.828 0.832 0.836 0.783 0.804 0.811 0.817 0.823 0.827 0.832 0.836 0.794 0.810 0.816 0.820 0.825 0.829 0.833 0.836

0.90 SB

PB BCPB

0.873 0.905 0.911 0.922 0.932 0.938 0.936 0.937 0.885 0.915 0.917 0.927 0.938 0.942 0.937 0.939 0.900 0.925 0.927 0.935 0.946 0.948 0.942 0.943 0.855 0.895 0.902 0.916 0.922 0.933 0.928 0.934

0.859 0.869 0.875 0.878 0.883 0.885 0.888 0.890 0.857 0.868 0.874 0.878 0.882 0.884 0.887 0.890 0.853 0.866 0.873 0.877 0.881 0.884 0.887 0.890 0.862 0.871 0.876 0.879 0.883 0.885 0.888 0.890

0.5 0.75 SB PB BCPB

0.907 0.918 0.929 0.938 0.936 0.940 0.939 0.943 0.916 0.923 0.936 0.941 0.940 0.942 0.942 0.943 0.927 0.930 0.940 0.945 0.944 0.945 0.945 0.946 0.898 0.911 0.923 0.934 0.932 0.934 0.935 0.941

0.659 0.687 0.698 0.704 0.713 0.718 0.724 0.730 0.656 0.686 0.697 0.703 0.712 0.717 0.723 0.729 0.651 0.683 0.696 0.702 0.711 0.717 0.723 0.729 0.663 0.689 0.700 0.705 0.713 0.718 0.724 0.730

0.80 SB

PB BCPB0

0.894 0.920 0.928 0.928 0.933 0.934 0.939 0.946 0.905 0.927 0.932 0.933 0.936 0.936 0.943 0.948 0.919 0.940 0.939 0.940 0.941 0.940 0.948 0.950 0.881 0.910 0.922 0.924 0.930 0.928 0.935 0.945

0.726 0.747 0.755 0.762 0.769 0.773 0.778 0.783 0.723 0.746 0.754 0.761 0.768 0.773 0.778 0.783 0.718 0.743 0.753 0.760 0.767 0.772 0.777 0.782 0.730 0.749 0.757 0.763 0.769 0.774 0.779 0.783

0.85 SB

PB BCPB

0.894 0.905 0.925 0.927 0.926 0.934 0.940 0.943 0.901 0.912 0.931 0.932 0.930 0.936 0.944 0.944 0.911 0.921 0.937 0.941 0.935 0.941 0.950 0.946 0.882 0.898 0.917 0.920 0.919 0.929 0.936 0.939

0.791 0.808 0.815 0.820 0.825 0.828 0.832 0.836 0.788 0.807 0.813 0.819 0.825 0.828 0.832 0.836 0.784 0.804 0.812 0.818 0.824 0.827 0.831 0.836 0.795 0.810 0.816 0.821 0.826 0.829 0.832 0.836

Table 31A. (continued)

 0.751 SB PB BCPB

0.912 0.923 0.933 0.930 0.934 0.939 0.943 0.946 0.920 0.930 0.939 0.934 0.939 0.940 0.944 0.948 0.931 0.938 0.943 0.938 0.942 0.943 0.947 0.950 0.902 0.914 0.926 0.926 0.929 0.935 0.941 0.945

0.662 0.686 0.698 0.704 0.713 0.717 0.724 0.729 0.658 0.684 0.696 0.703 0.712 0.717 0.723 0.729 0.654 0.682 0.695 0.702 0.711 0.716 0.723 0.729 0.665 0.688 0.699 0.705 0.713 0.718 0.724 0.730

0.80 SB

PB BCPB

0.895 0.914 0.924 0.929 0.934 0.930 0.939 0.944 0.903 0.921 0.931 0.935 0.937 0.935 0.941 0.946 0.917 0.935 0.939 0.942 0.943 0.938 0.945 0.950 0.884 0.906 0.918 0.920 0.928 0.927 0.937 0.942

0.727 0.747 0.757 0.763 0.769 0.774 0.778 0.783 0.723 0.745 0.756 0.762 0.768 0.774 0.778 0.783 0.719 0.742 0.755 0.760 0.767 0.773 0.778 0.782 0.730 0.748 0.759 0.764 0.769 0.774 0.779 0.783

0.85 SB

PB BCPB

0.887 0.909 0.922 0.924 0.928 0.935 0.942 0.939 0.897 0.917 0.929 0.930 0.934 0.939 0.947 0.940 0.910 0.930 0.938 0.939 0.939 0.946 0.950 0.943 0.875 0.903 0.916 0.918 0.923 0.930 0.939 0.936

0.791 0.808 0.815 0.820 0.825 0.828 0.833 0.836 0.788 0.806 0.814 0.819 0.825 0.828 0.832 0.836 0.784 0.803 0.813 0.818 0.824 0.827 0.832 0.836 0.794 0.809 0.817 0.821 0.826 0.829 0.833 0.837 Table 31B. Average bound and coverage percentage of 97.5% bootstrap for Weibull process with  ,10 3.6,



¹ ¹



   ^ 

 .

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

 _0.80 _SB PB BCPB

0.932 0.948 0.960 0.963 0.964 0.967 0.964 0.971 0.941 0.954 0.965 0.967 0.968 0.970 0.967 0.972 0.950 0.962 0.972 0.971 0.972 0.972 0.970 0.974 0.917 0.938 0.951 0.956 0.960 0.962 0.961 0.970

0.712 0.735 0.747 0.754 0.763 0.767 0.774 0.780 0.706 0.732 0.745 0.752 0.762 0.766 0.773 0.779 0.702 0.730 0.744 0.751 0.761 0.766 0.773 0.779 0.718 0.738 0.750 0.756 0.764 0.768 0.774 0.780

0.85 SB

PB BCPB

0.916 0.937 0.949 0.955 0.958 0.958 0.958 0.966 0.928 0.948 0.956 0.960 0.964 0.963 0.963 0.970 0.935 0.957 0.962 0.965 0.967 0.966 0.966 0.972 0.898 0.925 0.943 0.949 0.955 0.953 0.955 0.964

0.780 0.800 0.809 0.814 0.820 0.825 0.829 0.834 0.775 0.797 0.807 0.812 0.819 0.824 0.829 0.833 0.771 0.794 0.805 0.811 0.818 0.823 0.828 0.833 0.786 0.803 0.811 0.816 0.821 0.826 0.830 0.834

0.90 SB

PB BCPB

0.910 0.935 0.949 0.947 0.954 0.954 0.960 0.962 0.922 0.942 0.958 0.954 0.963 0.959 0.965 0.965 0.930 0.952 0.961 0.960 0.968 0.963 0.968 0.968 0.892 0.921 0.939 0.938 0.949 0.948 0.956 0.958

0.851 0.865 0.872 0.875 0.879 0.882 0.885 0.889 0.847 0.863 0.870 0.874 0.878 0.882 0.885 0.889 0.843 0.861 0.869 0.873 0.878 0.881 0.885 0.888 0.855 0.867 0.873 0.876 0.880 0.883 0.886 0.889

0.5 0.80 SB PB BCPB

0.921 0.941 0.953 0.957 0.960 0.964 0.966 0.968 0.933 0.950 0.957 0.961 0.965 0.967 0.968 0.971 0.943 0.956 0.963 0.965 0.969 0.971 0.970 0.973 0.904 0.933 0.947 0.952 0.956 0.962 0.964 0.967

0.713 0.737 0.747 0.755 0.763 0.767 0.773 0.779 0.708 0.734 0.745 0.753 0.762 0.766 0.773 0.779 0.703 0.732 0.743 0.752 0.761 0.765 0.772 0.779 0.720 0.741 0.749 0.757 0.764 0.767 0.774 0.780

0.85 SB

PB BCPB0

0.916 0.939 0.947 0.958 0.961 0.961 0.965 0.967 0.927 0.948 0.953 0.963 0.965 0.966 0.968 0.969 0.934 0.955 0.958 0.968 0.967 0.969 0.969 0.970 0.899 0.928 0.935 0.949 0.955 0.957 0.960 0.964

0.778 0.799 0.808 0.814 0.820 0.824 0.829 0.833 0.773 0.796 0.806 0.812 0.819 0.823 0.828 0.833 0.769 0.793 0.805 0.811 0.818 0.823 0.828 0.833 0.784 0.802 0.811 0.815 0.821 0.825 0.829 0.834

0.90 SB

PB BCPB

0.912 0.931 0.946 0.952 0.955 0.957 0.961 0.965 0.926 0.940 0.954 0.958 0.963 0.961 0.965 0.970 0.936 0.948 0.959 0.963 0.968 0.963 0.968 0.972 0.894 0.916 0.937 0.946 0.949 0.950 0.957 0.960

0.852 0.865 0.871 0.874 0.879 0.882 0.885 0.889 0.848 0.863 0.870 0.873 0.878 0.881 0.885 0.888 0.844 0.861 0.868 0.872 0.878 0.881 0.885 0.888 0.856 0.868 0.873 0.875 0.880 0.882 0.886 0.889

 0.801 SB PB BCPB

0.927 0.948 0.954 0.960 0.961 0.968 0.964 0.968 0.938 0.956 0.961 0.964 0.963 0.971 0.968 0.970 0.947 0.962 0.964 0.968 0.968 0.974 0.971 0.971 0.913 0.938 0.945 0.953 0.957 0.963 0.962 0.965

0.711 0.736 0.747 0.755 0.763 0.767 0.774 0.780 0.706 0.733 0.745 0.753 0.762 0.766 0.773 0.779 0.701 0.731 0.744 0.752 0.761 0.765 0.773 0.779 0.718 0.740 0.750 0.756 0.764 0.767 0.774 0.780

0.85 SB

PB BCPB0

0.910 0.945 0.951 0.952 0.957 0.963 0.962 0.970 0.925 0.951 0.961 0.960 0.963 0.966 0.966 0.973 0.933 0.960 0.966 0.965 0.965 0.971 0.969 0.976 0.893 0.932 0.941 0.946 0.952 0.957 0.958 0.967

0.780 0.800 0.807 0.813 0.820 0.824 0.829 0.833 0.775 0.797 0.805 0.812 0.819 0.823 0.828 0.833 0.770 0.794 0.803 0.810 0.818 0.823 0.828 0.833 0.786 0.803 0.809 0.815 0.821 0.825 0.829 0.834

0.90 SB

PB BCPB

0.908 0.927 0.939 0.943 0.955 0.961 0.964 0.965 0.922 0.936 0.947 0.954 0.961 0.964 0.968 0.967 0.931 0.944 0.952 0.959 0.964 0.968 0.970 0.971

0.851 0.864 0.871 0.875 0.879 0.882 0.885 0.888 0.847 0.862 0.870 0.873 0.878 0.881 0.885 0.888 0.843 0.860 0.868 0.872 0.877 0.881 0.884 0.888

Table 31B. (continued)

0.5 0.75 SB PB BCPB

0.933 0.952 0.960 0.964 0.964 0.967 0.970 0.974 0.947 0.961 0.964 0.969 0.968 0.969 0.973 0.977 0.953 0.967 0.968 0.973 0.969 0.972 0.975 0.978 0.923 0.944 0.953 0.961 0.958 0.962 0.966 0.971

0.643 0.674 0.687 0.694 0.705 0.711 0.718 0.725 0.637 0.671 0.685 0.693 0.704 0.710 0.718 0.725 0.633 0.668 0.684 0.692 0.704 0.710 0.718 0.725 0.649 0.677 0.689 0.696 0.706 0.712 0.719 0.726

0.80 SB

PB BCPB

0.927 0.947 0.953 0.956 0.958 0.966 0.963 0.970 0.940 0.954 0.962 0.962 0.961 0.967 0.967 0.974 0.947 0.957 0.966 0.967 0.965 0.970 0.968 0.975 0.911 0.938 0.950 0.950 0.955 0.963 0.960 0.966

0.712 0.736 0.747 0.755 0.763 0.768 0.773 0.780 0.707 0.733 0.745 0.753 0.762 0.767 0.773 0.779 0.702 0.731 0.743 0.752 0.761 0.767 0.772 0.779 0.718 0.739 0.749 0.756 0.764 0.769 0.774 0.780

0.85 SB

PB BCPB

0.909 0.943 0.951 0.955 0.960 0.963 0.962 0.968 0.921 0.950 0.955 0.958 0.964 0.966 0.964 0.971 0.930 0.956 0.962 0.963 0.969 0.970 0.967 0.973 0.890 0.929 0.941 0.948 0.954 0.959 0.960 0.963

0.781 0.800 0.809 0.814 0.820 0.825 0.829 0.834 0.776 0.797 0.807 0.812 0.819 0.824 0.828 0.833 0.771 0.794 0.805 0.811 0.818 0.823 0.828 0.833 0.787 0.803 0.811 0.815 0.821 0.826 0.829 0.834

 0.751 SB PB BCPB

0.943 0.952 0.959 0.963 0.967 0.968 0.967 0.974 0.951 0.958 0.965 0.966 0.972 0.971 0.969 0.975 0.957 0.962 0.970 0.969 0.973 0.973 0.971 0.976 0.928 0.943 0.952 0.958 0.964 0.964 0.964 0.971

0.644 0.673 0.688 0.695 0.705 0.711 0.719 0.725 0.639 0.670 0.686 0.694 0.704 0.711 0.718 0.725 0.634 0.668 0.685 0.693 0.703 0.710 0.718 0.725 0.650 0.676 0.690 0.697 0.706 0.712 0.719 0.726

0.80 SB

PB BCPB0

0.922 0.949 0.960 0.959 0.963 0.971 0.968 0.970 0.933 0.959 0.963 0.965 0.966 0.974 0.970 0.971 0.943 0.966 0.966 0.971 0.968 0.976 0.973 0.973 0.909 0.940 0.952 0.952 0.959 0.966 0.965 0.966

0.711 0.737 0.748 0.754 0.763 0.767 0.774 0.780 0.705 0.734 0.746 0.753 0.762 0.766 0.773 0.779 0.701 0.732 0.744 0.752 0.761 0.766 0.773 0.779 0.717 0.741 0.750 0.756 0.764 0.768 0.774 0.780

0.85 SB

PB BCPB

0.916 0.941 0.949 0.957 0.963 0.961 0.963 0.968 0.925 0.952 0.957 0.962 0.969 0.965 0.967 0.972 0.935 0.956 0.962 0.969 0.973 0.968 0.969 0.973 0.895 0.929 0.941 0.950 0.956 0.955 0.957 0.967

0.780 0.800 0.809 0.814 0.820 0.824 0.829 0.834 0.775 0.797 0.807 0.812 0.819 0.824 0.829 0.833 0.770 0.795 0.805 0.811 0.818 0.823 0.828 0.833 0.786 0.803 0.811 0.815 0.821 0.825 0.830 0.834 Table 32A. Average bound and coverage percentage of 95% bootstrap for Weibull process with  ,10  ,6



¹ ¹



   ^ 

 .

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

 _0.80 _SB PB BCPB

0.898 0.917 0.925 0.928 0.935 0.939 0.934 0.948 0.909 0.926 0.929 0.932 0.939 0.942 0.937 0.949 0.920 0.935 0.938 0.939 0.946 0.947 0.941 0.951 0.889 0.909 0.919 0.923 0.930 0.935 0.931 0.946

0.725 0.747 0.757 0.762 0.769 0.773 0.778 0.783 0.722 0.745 0.756 0.761 0.768 0.772 0.778 0.783 0.717 0.743 0.754 0.760 0.767 0.772 0.778 0.782 0.729 0.749 0.758 0.763 0.769 0.773 0.779 0.783

0.85 SB

PB BCPB

0.888 0.911 0.918 0.925 0.930 0.934 0.933 0.942 0.901 0.917 0.928 0.934 0.934 0.936 0.937 0.944 0.916 0.931 0.939 0.940 0.942 0.943 0.940 0.947 0.876 0.902 0.910 0.920 0.923 0.928 0.929 0.936

0.791 0.807 0.815 0.819 0.825 0.828 0.832 0.836 0.787 0.805 0.814 0.818 0.824 0.828 0.832 0.836 0.783 0.802 0.812 0.817 0.824 0.827 0.831 0.836 0.794 0.808 0.816 0.820 0.826 0.829 0.833 0.836

0.90 SB

PB BCPB

0.867 0.894 0.910 0.919 0.920 0.925 0.931 0.938 0.878 0.902 0.917 0.925 0.927 0.931 0.936 0.940 0.889 0.913 0.924 0.932 0.936 0.937 0.940 0.944 0.853 0.882 0.900 0.909 0.912 0.921 0.926 0.935

0.858 0.870 0.875 0.878 0.882 0.884 0.887 0.890 0.855 0.869 0.874 0.878 0.881 0.884 0.887 0.890 0.851 0.867 0.872 0.876 0.880 0.883 0.887 0.890 0.861 0.872 0.876 0.879 0.882 0.885 0.888 0.890

0.5 0.80 SB PB BCPB

0.892 0.916 0.922 0.928 0.932 0.937 0.936 0.942 0.904 0.924 0.929 0.931 0.936 0.939 0.940 0.945 0.914 0.933 0.939 0.942 0.943 0.945 0.944 0.948 0.881 0.908 0.916 0.921 0.927 0.933 0.933 0.939

0.724 0.745 0.756 0.761 0.768 0.772 0.778 0.783 0.721 0.743 0.754 0.760 0.767 0.771 0.777 0.782 0.716 0.740 0.753 0.759 0.766 0.771 0.777 0.782 0.728 0.747 0.757 0.762 0.769 0.772 0.778 0.783

0.85 SB

PB BCPB0

0.888 0.912 0.921 0.922 0.929 0.932 0.937 0.939 0.898 0.919 0.928 0.929 0.934 0.936 0.942 0.943 0.913 0.930 0.938 0.937 0.941 0.940 0.947 0.945 0.873 0.902 0.911 0.913 0.924 0.928 0.931 0.935

0.789 0.805 0.814 0.819 0.824 0.827 0.831 0.836 0.786 0.803 0.812 0.818 0.823 0.827 0.831 0.836 0.781 0.801 0.810 0.816 0.822 0.826 0.831 0.835 0.793 0.807 0.815 0.820 0.825 0.828 0.832 0.836

0.90 SB

PB BCPB

0.860 0.886 0.908 0.914 0.918 0.927 0.934 0.938 0.872 0.899 0.917 0.923 0.925 0.935 0.939 0.941 0.887 0.909 0.930 0.931 0.931 0.943 0.943 0.944 0.841 0.873 0.896 0.906 0.911 0.920 0.928 0.935

0.858 0.868 0.873 0.877 0.881 0.883 0.886 0.889 0.855 0.866 0.872 0.876 0.880 0.883 0.886 0.889 0.851 0.864 0.870 0.874 0.879 0.882 0.886 0.889 0.861 0.870 0.875 0.878 0.881 0.884 0.887 0.889

Table 32A. (continued)

 0.801 SB PB BCPB

0.896 0.911 0.921 0.931 0.934 0.935 0.939 0.940 0.905 0.918 0.926 0.935 0.938 0.939 0.941 0.942 0.918 0.927 0.934 0.941 0.943 0.946 0.944 0.947 0.885 0.901 0.918 0.923 0.931 0.932 0.937 0.938

0.721 0.746 0.753 0.760 0.768 0.772 0.777 0.782 0.717 0.744 0.752 0.759 0.767 0.771 0.776 0.782 0.712 0.741 0.750 0.758 0.766 0.770 0.776 0.782 0.725 0.748 0.755 0.761 0.768 0.772 0.777 0.783

0.85 SB

PB BCPB

0.887 0.904 0.914 0.922 0.928 0.929 0.938 0.938 0.903 0.913 0.922 0.929 0.933 0.933 0.942 0.942 0.916 0.925 0.933 0.935 0.941 0.940 0.949 0.948 0.873 0.895 0.903 0.915 0.922 0.923 0.935 0.935

0.787 0.805 0.812 0.817 0.823 0.827 0.831 0.835 0.784 0.803 0.811 0.816 0.823 0.827 0.831 0.835 0.779 0.800 0.809 0.815 0.822 0.826 0.830 0.835 0.791 0.807 0.814 0.818 0.824 0.828 0.831 0.835

0.90 SB

PB BCPB

0.863 0.895 0.910 0.914 0.926 0.934 0.931 0.936 0.876 0.905 0.916 0.922 0.934 0.938 0.939 0.938 0.891 0.919 0.926 0.932 0.941 0.943 0.947 0.943 0.846 0.885 0.898 0.905 0.921 0.926 0.926 0.933

0.856 0.868 0.872 0.877 0.880 0.883 0.886 0.889 0.853 0.866 0.871 0.876 0.880 0.883 0.886 0.889 0.849 0.864 0.869 0.875 0.879 0.882 0.886 0.889 0.859 0.870 0.874 0.878 0.881 0.884 0.887 0.889

0.5 0.80 SB PB BCPB

0.899 0.919 0.932 0.933 0.932 0.940 0.940 0.948 0.909 0.927 0.938 0.938 0.935 0.943 0.941 0.950 0.922 0.935 0.944 0.945 0.940 0.947 0.944 0.952 0.885 0.909 0.926 0.929 0.928 0.933 0.936 0.946

0.728 0.748 0.757 0.762 0.770 0.773 0.778 0.783 0.725 0.747 0.755 0.761 0.769 0.773 0.778 0.783 0.720 0.744 0.754 0.760 0.768 0.772 0.778 0.783 0.731 0.750 0.758 0.763 0.771 0.774 0.779 0.783

0.85 SB

PB BCPB0

0.887 0.911 0.920 0.928 0.930 0.934 0.941 0.943 0.897 0.917 0.927 0.933 0.935 0.939 0.943 0.947 0.913 0.926 0.935 0.940 0.941 0.944 0.948 0.950 0.875 0.902 0.912 0.921 0.924 0.929 0.938 0.941

0.793 0.809 0.815 0.821 0.826 0.829 0.833 0.837 0.790 0.807 0.814 0.820 0.825 0.828 0.833 0.836 0.785 0.805 0.812 0.819 0.824 0.828 0.832 0.836 0.796 0.811 0.816 0.822 0.826 0.829 0.833 0.837

0.90 SB

PB BCPB

0.870 0.903 0.921 0.921 0.925 0.931 0.934 0.936 0.883 0.909 0.926 0.925 0.932 0.935 0.937 0.938 0.897 0.917 0.933 0.933 0.938 0.941 0.942 0.943 0.855 0.893 0.912 0.915 0.916 0.925 0.931 0.934

0.861 0.872 0.876 0.880 0.883 0.885 0.888 0.891 0.859 0.871 0.875 0.879 0.883 0.885 0.888 0.891 0.856 0.869 0.873 0.878 0.882 0.884 0.887 0.890 0.864 0.873 0.877 0.880 0.884 0.886 0.888 0.891

 0.801 SB PB BCPB

0.904 0.921 0.926 0.927 0.938 0.937 0.942 0.947 0.912 0.930 0.930 0.934 0.941 0.940 0.945 0.948 0.924 0.938 0.937 0.940 0.945 0.944 0.949 0.951 0.892 0.909 0.921 0.922 0.934 0.933 0.940 0.946

0.728 0.749 0.759 0.764 0.770 0.774 0.779 0.783 0.725 0.747 0.758 0.763 0.770 0.774 0.778 0.783 0.721 0.745 0.756 0.762 0.769 0.773 0.778 0.783 0.731 0.750 0.760 0.765 0.771 0.775 0.779 0.784

0.85 SB

PB BCPB0

0.891 0.912 0.922 0.931 0.930 0.933 0.934 0.939 0.899 0.920 0.927 0.936 0.933 0.937 0.939 0.942 0.910 0.931 0.939 0.944 0.938 0.941 0.945 0.945 0.876 0.902 0.916 0.925 0.925 0.929 0.931 0.936

0.795 0.811 0.817 0.822 0.827 0.830 0.834 0.837 0.792 0.809 0.816 0.821 0.826 0.829 0.833 0.837 0.789 0.807 0.814 0.820 0.826 0.829 0.833 0.837 0.798 0.812 0.818 0.823 0.827 0.830 0.834 0.837

0.90 SB

PB BCPB

0.893 0.901 0.918 0.922 0.930 0.931 0.930 0.938 0.906 0.913 0.923 0.927 0.935 0.936 0.933 0.941 0.918 0.922 0.930 0.934 0.939 0.940 0.938 0.945 0.883 0.889 0.912 0.917 0.924 0.927 0.926 0.935

0.861 0.873 0.877 0.881 0.884 0.886 0.889 0.891 0.859 0.872 0.877 0.880 0.883 0.886 0.889 0.891 0.857 0.871 0.876 0.880 0.883 0.886 0.888 0.891 0.864 0.875 0.878 0.882 0.884 0.887 0.889 0.891 Table 32B. Average bound and coverage percentage of 97.5% bootstrap for Weibull process with  ,10  ,6



¹ ¹



   ^ .

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

 _0.80 _SB PB BCPB

0.931 0.945 0.956 0.957 0.960 0.966 0.967 0.968 0.941 0.954 0.962 0.960 0.966 0.969 0.970 0.970 0.949 0.960 0.966 0.965 0.969 0.972 0.972 0.971 0.913 0.936 0.948 0.948 0.955 0.963 0.962 0.965

0.711 0.737 0.748 0.754 0.763 0.767 0.773 0.779 0.705 0.734 0.746 0.752 0.762 0.766 0.773 0.779 0.700 0.732 0.744 0.751 0.761 0.765 0.772 0.779 0.717 0.741 0.750 0.756 0.764 0.768 0.774 0.780

0.85 SB

PB BCPB

0.917 0.936 0.949 0.955 0.959 0.966 0.966 0.969 0.927 0.948 0.958 0.960 0.966 0.973 0.969 0.972 0.938 0.957 0.962 0.964 0.970 0.976 0.971 0.972 0.897 0.921 0.941 0.947 0.954 0.961 0.960 0.966

0.779 0.800 0.808 0.814 0.819 0.824 0.829 0.833 0.774 0.797 0.806 0.812 0.818 0.823 0.828 0.833 0.769 0.794 0.805 0.811 0.817 0.823 0.828 0.833 0.786 0.803 0.810 0.815 0.820 0.825 0.829 0.834

0.90 SB

PB BCPB

0.901 0.922 0.940 0.942 0.952 0.956 0.960 0.960 0.913 0.929 0.948 0.950 0.959 0.961 0.964 0.966 0.926 0.937 0.954 0.956 0.964 0.965 0.970 0.969

0.851 0.864 0.870 0.874 0.879 0.881 0.885 0.888 0.847 0.861 0.869 0.873 0.878 0.880 0.884 0.888 0.843 0.859 0.867 0.872 0.877 0.880 0.884 0.888

Table 32B. (continued)

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

0.5 0.80 SB PB BCPB

0.918 0.940 0.950 0.955 0.960 0.965 0.967 0.968 0.929 0.951 0.957 0.961 0.964 0.969 0.972 0.968 0.940 0.959 0.962 0.966 0.966 0.971 0.976 0.970 0.899 0.926 0.942 0.948 0.956 0.961 0.963 0.964

0.710 0.736 0.747 0.754 0.762 0.767 0.773 0.779 0.705 0.733 0.745 0.752 0.761 0.766 0.772 0.779 0.700 0.730 0.743 0.751 0.760 0.765 0.772 0.779 0.717 0.739 0.749 0.755 0.764 0.768 0.773 0.780

0.85 SB

PB BCPB

0.913 0.932 0.945 0.952 0.957 0.959 0.961 0.963 0.925 0.944 0.952 0.960 0.963 0.964 0.965 0.966 0.935 0.954 0.955 0.965 0.967 0.968 0.970 0.968 0.893 0.922 0.934 0.941 0.950 0.952 0.956 0.959

0.777 0.798 0.807 0.813 0.820 0.823 0.828 0.833 0.771 0.795 0.805 0.811 0.819 0.822 0.828 0.833 0.766 0.792 0.803 0.810 0.818 0.822 0.827 0.832 0.783 0.802 0.809 0.815 0.821 0.824 0.829 0.833

0.90 SB

PB BCPB

0.894 0.923 0.936 0.950 0.952 0.955 0.961 0.964 0.908 0.937 0.945 0.956 0.956 0.958 0.964 0.969 0.918 0.943 0.953 0.964 0.960 0.963 0.966 0.971 0.872 0.905 0.923 0.940 0.942 0.948 0.955 0.960

0.849 0.862 0.869 0.873 0.878 0.880 0.884 0.888 0.844 0.860 0.867 0.871 0.877 0.879 0.883 0.887 0.840 0.857 0.865 0.870 0.876 0.879 0.883 0.887 0.854 0.866 0.871 0.875 0.879 0.881 0.884 0.888

 0.801 SB PB BCPB

0.926 0.947 0.952 0.954 0.961 0.963 0.963 0.969 0.936 0.955 0.961 0.957 0.968 0.967 0.966 0.971 0.944 0.960 0.963 0.962 0.972 0.969 0.969 0.974 0.911 0.932 0.945 0.945 0.955 0.958 0.960 0.968

0.708 0.732 0.747 0.753 0.762 0.766 0.773 0.779 0.702 0.729 0.744 0.751 0.761 0.766 0.772 0.778 0.697 0.726 0.743 0.750 0.760 0.765 0.772 0.778 0.715 0.736 0.749 0.754 0.763 0.767 0.773 0.779

0.85 SB

PB BCPB0

0.908 0.941 0.943 0.949 0.958 0.961 0.963 0.968 0.918 0.951 0.954 0.957 0.965 0.965 0.967 0.970 0.929 0.956 0.961 0.960 0.969 0.967 0.970 0.971 0.886 0.928 0.933 0.939 0.949 0.955 0.962 0.965

0.775 0.795 0.805 0.811 0.819 0.823 0.828 0.832 0.769 0.792 0.803 0.809 0.818 0.822 0.827 0.832 0.763 0.789 0.801 0.808 0.817 0.821 0.827 0.832 0.782 0.799 0.807 0.813 0.820 0.824 0.828 0.833

0.90 SB

PB BCPB

0.892 0.923 0.939 0.941 0.955 0.959 0.957 0.965 0.908 0.934 0.948 0.949 0.962 0.966 0.963 0.968 0.918 0.942 0.957 0.957 0.967 0.970 0.966 0.971 0.871 0.909 0.924 0.929 0.946 0.951 0.954 0.961

0.848 0.860 0.868 0.872 0.877 0.880 0.884 0.888 0.843 0.857 0.866 0.870 0.876 0.880 0.883 0.887 0.839 0.855 0.864 0.869 0.875 0.879 0.883 0.887 0.854 0.864 0.870 0.873 0.878 0.881 0.884 0.888

0.5 0.80 SB PB BCPB

0.929 0.952 0.956 0.961 0.961 0.964 0.967 0.967 0.940 0.959 0.965 0.967 0.965 0.967 0.971 0.969 0.948 0.962 0.970 0.970 0.968 0.969 0.973 0.970 0.914 0.942 0.951 0.956 0.956 0.960 0.964 0.964

0.711 0.738 0.748 0.755 0.764 0.769 0.774 0.780 0.706 0.735 0.746 0.753 0.763 0.768 0.773 0.780 0.701 0.733 0.745 0.752 0.762 0.767 0.773 0.780 0.717 0.741 0.750 0.756 0.765 0.770 0.774 0.781

0.85 SB

PB BCPB0

0.921 0.943 0.952 0.956 0.960 0.965 0.968 0.972 0.932 0.951 0.956 0.959 0.967 0.969 0.972 0.974 0.943 0.955 0.961 0.963 0.970 0.972 0.973 0.977 0.907 0.936 0.943 0.951 0.952 0.957 0.964 0.970

0.781 0.800 0.810 0.814 0.821 0.825 0.830 0.834 0.776 0.797 0.808 0.813 0.820 0.824 0.829 0.833 0.772 0.794 0.806 0.812 0.819 0.823 0.829 0.833 0.786 0.803 0.812 0.816 0.822 0.826 0.830 0.834

0.90 SB

PB BCPB

0.906 0.935 0.949 0.954 0.958 0.958 0.964 0.968 0.919 0.945 0.955 0.961 0.964 0.962 0.968 0.971 0.929 0.952 0.959 0.966 0.968 0.966 0.972 0.973 0.891 0.920 0.937 0.941 0.951 0.951 0.958 0.964

0.853 0.866 0.871 0.875 0.880 0.883 0.886 0.889 0.850 0.864 0.870 0.874 0.879 0.882 0.885 0.889 0.846 0.862 0.868 0.873 0.878 0.881 0.885 0.888 0.858 0.868 0.873 0.876 0.880 0.883 0.886 0.889

 0.801 SB PB BCPB

0.933 0.944 0.957 0.959 0.965 0.968 0.972 0.968 0.944 0.951 0.965 0.963 0.968 0.970 0.974 0.970 0.950 0.958 0.970 0.966 0.971 0.973 0.975 0.971 0.917 0.934 0.949 0.953 0.960 0.965 0.971 0.966

0.715 0.741 0.750 0.756 0.765 0.769 0.775 0.780 0.710 0.738 0.748 0.755 0.764 0.768 0.774 0.780 0.706 0.736 0.747 0.754 0.763 0.768 0.774 0.780 0.720 0.743 0.752 0.758 0.766 0.770 0.775 0.781

0.85 SB

PB BCPB0

0.926 0.943 0.950 0.957 0.959 0.960 0.965 0.967 0.937 0.951 0.958 0.960 0.963 0.963 0.970 0.968 0.942 0.958 0.962 0.964 0.967 0.966 0.971 0.970 0.912 0.932 0.941 0.951 0.951 0.958 0.964 0.965

0.783 0.802 0.811 0.816 0.822 0.826 0.830 0.835 0.779 0.800 0.809 0.815 0.821 0.826 0.830 0.834 0.775 0.798 0.808 0.814 0.820 0.825 0.829 0.834 0.788 0.805 0.813 0.818 0.823 0.827 0.831 0.835

0.90 SB

PB BCPB

0.914 0.935 0.959 0.956 0.960 0.960 0.966 0.964 0.927 0.946 0.965 0.961 0.967 0.962 0.970 0.966 0.935 0.953 0.968 0.966 0.970 0.965 0.973 0.968 0.902 0.925 0.951 0.950 0.954 0.954 0.961 0.959

0.856 0.868 0.873 0.877 0.881 0.884 0.887 0.890 0.853 0.866 0.872 0.876 0.880 0.883 0.886 0.890 0.851 0.865 0.871 0.876 0.880 0.883 0.886 0.889 0.860 0.870 0.875 0.878 0.882 0.884 0.887 0.890

Table 33A. Average bound and coverage percentage of 95% bootstrap for Weibull process with  ,10  ,10



¹ ¹



   ^ .

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

 0.80 SB PB BCPB

0.893 0.921 0.932 0.927 0.934 0.942 0.931 0.944 0.903 0.928 0.938 0.929 0.939 0.945 0.934 0.946 0.913 0.936 0.943 0.935 0.946 0.948 0.939 0.948 0.874 0.911 0.927 0.921 0.931 0.938 0.928 0.943

0.728 0.748 0.755 0.762 0.769 0.773 0.778 0.783 0.724 0.746 0.754 0.761 0.768 0.772 0.778 0.783 0.720 0.743 0.753 0.760 0.767 0.772 0.778 0.782 0.731 0.750 0.757 0.763 0.769 0.773 0.779 0.783

0.85 SB

PB BCPB

0.888 0.909 0.922 0.925 0.927 0.931 0.937 0.937 0.898 0.918 0.932 0.932 0.934 0.936 0.942 0.939 0.912 0.932 0.939 0.939 0.942 0.942 0.946 0.944 0.874 0.902 0.911 0.919 0.920 0.925 0.935 0.935

0.791 0.807 0.815 0.819 0.825 0.828 0.833 0.836 0.788 0.805 0.814 0.818 0.825 0.828 0.832 0.836 0.783 0.802 0.812 0.817 0.824 0.827 0.832 0.836 0.794 0.809 0.816 0.820 0.826 0.829 0.833 0.836

0.90 SB

PB BCPB

0.857 0.886 0.907 0.917 0.909 0.926 0.928 0.935 0.869 0.896 0.913 0.925 0.915 0.931 0.932 0.939 0.883 0.905 0.923 0.936 0.922 0.940 0.937 0.943 0.841 0.879 0.896 0.909 0.902 0.918 0.921 0.932

0.857 0.870 0.874 0.878 0.881 0.884 0.887 0.890 0.854 0.868 0.873 0.877 0.881 0.884 0.887 0.889 0.850 0.865 0.871 0.875 0.880 0.883 0.886 0.889 0.860 0.871 0.875 0.879 0.882 0.885 0.887 0.890

0.5 0.80 SB PB BCPB

0.894 0.918 0.924 0.931 0.940 0.936 0.942 0.934 0.903 0.923 0.929 0.935 0.944 0.939 0.943 0.937 0.913 0.934 0.937 0.942 0.949 0.944 0.947 0.940 0.879 0.907 0.916 0.928 0.935 0.934 0.939 0.934

0.72 0.743 0.754 0.76 0.767 0.771 0.776 0.782 0.716 0.741 0.753 0.759 0.766 0.771 0.776 0.782 0.711 0.738 0.751 0.757 0.765 0.77 0.775 0.782 0.724 0.745 0.756 0.761 0.767 0.772 0.776 0.782

0.85 SB

PB BCPB0

0.888 0.904 0.910 0.924 0.925 0.927 0.925 0.944 0.901 0.913 0.916 0.930 0.931 0.932 0.929 0.946 0.915 0.925 0.926 0.940 0.939 0.936 0.936 0.950 0.873 0.890 0.901 0.919 0.919 0.921 0.924 0.941

0.786 0.804 0.813 0.817 0.823 0.827 0.831 0.835 0.782 0.802 0.811 0.816 0.822 0.826 0.831 0.835 0.777 0.799 0.809 0.814 0.821 0.826 0.830 0.834 0.790 0.806 0.814 0.818 0.824 0.827 0.831 0.835

0.90 SB

PB BCPB

0.852 0.889 0.901 0.910 0.921 0.935 0.931 0.938 0.864 0.901 0.911 0.917 0.925 0.940 0.934 0.943 0.879 0.916 0.925 0.927 0.933 0.947 0.941 0.946 0.833 0.878 0.891 0.900 0.912 0.928 0.926 0.935

0.853 0.865 0.871 0.876 0.880 0.882 0.885 0.889 0.850 0.863 0.869 0.874 0.879 0.881 0.885 0.888 0.844 0.861 0.868 0.873 0.878 0.880 0.884 0.888 0.857 0.868 0.872 0.877 0.880 0.882 0.886 0.889

 0.801 SB PB BCPB

0.898 0.917 0.922 0.929 0.933 0.941 0.944 0.937 0.909 0.926 0.927 0.933 0.938 0.943 0.945 0.939 0.922 0.938 0.936 0.938 0.943 0.945 0.949 0.942 0.883 0.909 0.916 0.921 0.929 0.937 0.942 0.933

0.722 0.743 0.753 0.760 0.766 0.771 0.777 0.782 0.718 0.741 0.752 0.759 0.766 0.770 0.776 0.781 0.713 0.739 0.750 0.758 0.765 0.770 0.776 0.781 0.726 0.745 0.755 0.761 0.767 0.771 0.777 0.782

0.85 SB

PB BCPB0

0.878 0.903 0.913 0.923 0.925 0.931 0.932 0.936 0.889 0.913 0.922 0.929 0.930 0.936 0.937 0.940 0.907 0.927 0.930 0.937 0.938 0.942 0.940 0.942 0.861 0.890 0.904 0.914 0.918 0.926 0.929 0.936

0.788 0.805 0.812 0.817 0.823 0.827 0.831 0.835 0.784 0.804 0.811 0.816 0.822 0.826 0.831 0.835 0.779 0.801 0.809 0.814 0.822 0.826 0.830 0.835 0.792 0.808 0.814 0.818 0.824 0.827 0.831 0.836

0.90 SB

PB BCPB

0.862 0.891 0.902 0.911 0.922 0.929 0.932 0.932 0.873 0.902 0.911 0.917 0.931 0.933 0.935 0.937 0.886 0.914 0.924 0.929 0.939 0.941 0.942 0.943 0.845 0.878 0.888 0.900 0.912 0.923 0.925 0.930

0.855 0.867 0.873 0.876 0.881 0.883 0.886 0.889 0.852 0.865 0.872 0.875 0.880 0.882 0.886 0.889 0.847 0.862 0.870 0.874 0.879 0.881 0.885 0.889 0.858 0.869 0.874 0.877 0.881 0.883 0.886 0.889

0.5 0.80 SB PB BCPB

0.893 0.920 0.926 0.934 0.936 0.936 0.946 0.945 0.903 0.925 0.930 0.940 0.940 0.939 0.949 0.946 0.916 0.933 0.936 0.944 0.943 0.942 0.953 0.949 0.883 0.913 0.918 0.929 0.931 0.932 0.943 0.943

0.732 0.750 0.760 0.764 0.771 0.775 0.779 0.784 0.729 0.749 0.759 0.764 0.770 0.774 0.779 0.784 0.725 0.747 0.757 0.763 0.770 0.774 0.778 0.783 0.735 0.752 0.761 0.765 0.772 0.775 0.779 0.784

0.85 SB

PB BCPB0

0.890 0.908 0.921 0.928 0.928 0.932 0.935 0.939 0.899 0.917 0.926 0.934 0.933 0.936 0.937 0.941 0.911 0.927 0.934 0.941 0.939 0.941 0.942 0.945 0.877 0.899 0.913 0.922 0.924 0.928 0.932 0.937

0.796 0.811 0.818 0.822 0.827 0.830 0.834 0.837 0.793 0.809 0.817 0.821 0.827 0.830 0.834 0.837 0.789 0.807 0.816 0.820 0.826 0.829 0.833 0.837 0.799 0.812 0.819 0.823 0.828 0.830 0.834 0.838

0.90 SB

PB BCPB

0.879 0.899 0.917 0.917 0.927 0.925 0.933 0.937 0.887 0.908 0.921 0.924 0.934 0.931 0.937 0.940 0.897 0.917 0.929 0.931 0.938 0.936 0.942 0.943 0.867 0.888 0.910 0.913 0.920 0.920 0.930 0.933

0.864 0.873 0.877 0.881 0.884 0.886 0.889 0.891 0.862 0.872 0.877 0.880 0.884 0.886 0.888 0.891 0.859 0.870 0.875 0.879 0.883 0.886 0.888 0.891 0.866 0.875 0.878 0.882 0.885 0.887 0.889 0.891

Table 33A. (continued)

 0.801 SB PB BCPB

0.903 0.923 0.929 0.932 0.935 0.938 0.940 0.948 0.909 0.927 0.933 0.937 0.939 0.940 0.941 0.950 0.918 0.933 0.943 0.943 0.941 0.945 0.944 0.952 0.892 0.912 0.921 0.928 0.929 0.936 0.937 0.947

0.736 0.754 0.762 0.767 0.773 0.776 0.780 0.785 0.733 0.752 0.761 0.766 0.773 0.776 0.780 0.785 0.730 0.751 0.760 0.765 0.772 0.775 0.780 0.785 0.738 0.755 0.763 0.768 0.774 0.777 0.781 0.785

0.85 SB

PB BCPB

0.899 0.915 0.925 0.931 0.934 0.935 0.939 0.940 0.907 0.922 0.930 0.935 0.938 0.939 0.941 0.941 0.917 0.931 0.936 0.941 0.944 0.944 0.944 0.945 0.887 0.907 0.919 0.926 0.928 0.932 0.935 0.938

0.801 0.815 0.821 0.825 0.829 0.832 0.835 0.839 0.799 0.814 0.820 0.824 0.829 0.832 0.835 0.838 0.796 0.812 0.819 0.824 0.828 0.831 0.835 0.838 0.803 0.816 0.822 0.825 0.829 0.832 0.836 0.839

0.90 SB

PB BCPB

0.894 0.912 0.919 0.928 0.935 0.941 0.939 0.941 0.900 0.922 0.924 0.934 0.936 0.943 0.941 0.943 0.914 0.929 0.930 0.941 0.940 0.947 0.943 0.946 0.886 0.903 0.912 0.920 0.931 0.937 0.936 0.937

0.868 0.876 0.881 0.883 0.886 0.888 0.890 0.892 0.866 0.876 0.880 0.882 0.886 0.888 0.890 0.892 0.864 0.875 0.880 0.882 0.885 0.888 0.890 0.892 0.869 0.877 0.881 0.883 0.886 0.888 0.891 0.892 Table 33B. Average bound and coverage percentage of 97.5% bootstrap for Weibull process with  ,10  ,10



¹ ¹



   ^ 

 .

T Y_c bootstrap

(Coverage percentage ) Samples Size( n ) 25 50 75 100 150 200 300 500

(Average bound) Samples Size( n ) 25 50 75 100 150 200 300 500

 _0.80 _SB PB BCPB

0.928 0.944 0.956 0.957 0.965 0.965 0.963 0.967 0.937 0.954 0.962 0.960 0.969 0.968 0.965 0.970 0.945 0.961 0.966 0.964 0.973 0.971 0.967 0.972 0.916 0.930 0.947 0.948 0.960 0.961 0.961 0.964

0.712 0.737 0.747 0.754 0.763 0.767 0.774 0.779 0.706 0.734 0.745 0.753 0.762 0.766 0.773 0.779 0.702 0.732 0.744 0.751 0.761 0.766 0.773 0.779 0.718 0.741 0.749 0.756 0.764 0.768 0.774 0.780

0.85 SB

PB BCPB

0.915 0.932 0.945 0.952 0.958 0.966 0.964 0.966 0.928 0.943 0.956 0.956 0.963 0.972 0.968 0.970 0.935 0.951 0.961 0.961 0.965 0.974 0.970 0.972 0.897 0.921 0.940 0.945 0.951 0.958 0.961 0.964

0.780 0.800 0.808 0.813 0.819 0.824 0.829 0.834 0.775 0.797 0.806 0.812 0.818 0.823 0.828 0.833 0.770 0.795 0.805 0.811 0.817 0.822 0.828 0.833 0.786 0.803 0.811 0.815 0.820 0.825 0.829 0.834

0.90 SB

PB BCPB

0.887 0.918 0.939 0.934 0.947 0.957 0.959 0.959 0.901 0.930 0.946 0.944 0.955 0.962 0.964 0.964 0.911 0.941 0.951 0.950 0.959 0.967 0.968 0.967 0.867 0.903 0.923 0.923 0.939 0.951 0.954 0.955

0.850 0.864 0.869 0.873 0.878 0.881 0.884 0.888 0.845 0.861 0.867 0.872 0.877 0.880 0.884 0.888 0.841 0.858 0.866 0.871 0.876 0.880 0.883 0.887 0.855 0.867 0.872 0.875 0.879 0.882 0.885 0.888

0.5 0.80 SB PB BCPB

0.922 0.943 0.952 0.957 0.960 0.969 0.967 0.965 0.932 0.954 0.958 0.962 0.966 0.973 0.970 0.968 0.942 0.961 0.962 0.968 0.968 0.976 0.972 0.969 0.902 0.934 0.945 0.946 0.956 0.964 0.965 0.962

0.707 0.732 0.745 0.753 0.760 0.766 0.772 0.779 0.701 0.729 0.743 0.751 0.759 0.765 0.771 0.778 0.696 0.726 0.741 0.750 0.758 0.764 0.771 0.778 0.714 0.735 0.747 0.754 0.762 0.767 0.773 0.779

0.85 SB

PB BCPB0

0.910 0.935 0.942 0.95 0.957 0.956 0.959 0.965 0.920 0.946 0.952 0.958 0.963 0.962 0.962 0.969 0.929 0.954 0.960 0.964 0.966 0.965 0.966 0.971 0.894 0.922 0.930 0.938 0.951 0.951 0.955 0.962

0.774 0.794 0.805 0.811 0.818 0.822 0.827 0.832 0.768 0.791 0.803 0.809 0.817 0.821 0.826 0.832 0.762 0.788 0.801 0.808 0.816 0.820 0.826 0.831 0.781 0.798 0.808 0.813 0.819 0.823 0.828 0.832

0.90 SB

PB BCPB

0.877 0.916 0.931 0.946 0.949 0.950 0.963 0.967 0.889 0.927 0.943 0.956 0.955 0.958 0.968 0.970 0.900 0.937 0.951 0.961 0.962 0.961 0.973 0.972 0.854 0.899 0.913 0.931 0.939 0.942 0.955 0.962

0.844 0.858 0.866 0.870 0.875 0.879 0.882 0.887 0.839 0.855 0.863 0.868 0.874 0.878 0.882 0.886 0.833 0.852 0.861 0.867 0.873 0.877 0.881 0.886 0.851 0.862 0.868 0.872 0.877 0.880 0.883 0.887

 0.801 SB PB BCPB

0.920 0.941 0.949 0.959 0.966 0.960 0.969 0.965 0.931 0.952 0.954 0.964 0.971 0.965 0.972 0.968 0.944 0.960 0.961 0.968 0.973 0.968 0.973 0.971 0.905 0.928 0.941 0.953 0.960 0.957 0.966 0.962

0.707 0.732 0.745 0.752 0.760 0.765 0.772 0.778 0.701 0.728 0.743 0.750 0.759 0.765 0.771 0.778 0.695 0.726 0.741 0.749 0.758 0.764 0.771 0.778 0.713 0.735 0.748 0.754 0.761 0.766 0.772 0.779

0.85 SB

PB BCPB0

0.908 0.929 0.946 0.950 0.957 0.959 0.960 0.964 0.924 0.940 0.954 0.957 0.961 0.963 0.966 0.966 0.931 0.947 0.960 0.963 0.966 0.966 0.968 0.969 0.891 0.915 0.931 0.943 0.949 0.955 0.955 0.960

0.775 0.796 0.806 0.811 0.818 0.822 0.827 0.833 0.769 0.793 0.803 0.809 0.817 0.821 0.827 0.832 0.764 0.790 0.801 0.808 0.816 0.820 0.826 0.832 0.782 0.800 0.808 0.812 0.819 0.823 0.828 0.833

0.90 SB

PB BCPB

0.891 0.919 0.937 0.942 0.953 0.957 0.957 0.962 0.906 0.931 0.946 0.951 0.960 0.961 0.963 0.965 0.918 0.943 0.955 0.958 0.963 0.966 0.966 0.967 0.866 0.904 0.923 0.932 0.941 0.948 0.949 0.957

0.847 0.861 0.867 0.872 0.877 0.879 0.883 0.887 0.842 0.858 0.865 0.870 0.876 0.879 0.883 0.887 0.837 0.855 0.864 0.869 0.875 0.878 0.882 0.886 0.853 0.864 0.870 0.873 0.878 0.880 0.884 0.887

Table 33B. (continued)

0.5 0.80 SB PB BCPB

0.928 0.944 0.959 0.963 0.965 0.967 0.969 0.971 0.937 0.952 0.964 0.969 0.968 0.970 0.972 0.973 0.945 0.957 0.966 0.972 0.969 0.971 0.973 0.975 0.915 0.935 0.952 0.958 0.961 0.965 0.967 0.967

0.717 0.739 0.750 0.756 0.765 0.769 0.775 0.781 0.712 0.737 0.748 0.755 0.764 0.769 0.774 0.780 0.708 0.734 0.746 0.754 0.764 0.768 0.774 0.780 0.722 0.742 0.751 0.758 0.766 0.770 0.775 0.781

0.85 SB

PB BCPB

0.923 0.944 0.950 0.954 0.960 0.964 0.966 0.967 0.933 0.952 0.958 0.961 0.964 0.967 0.968 0.969 0.941 0.959 0.963 0.965 0.968 0.969 0.969 0.970 0.907 0.930 0.942 0.946 0.956 0.960 0.963 0.961

0.785 0.803 0.811 0.817 0.822 0.826 0.831 0.835 0.780 0.801 0.810 0.815 0.821 0.825 0.830 0.835 0.777 0.799 0.808 0.814 0.821 0.825 0.830 0.834 0.790 0.806 0.813 0.818 0.823 0.827 0.831 0.835

0.90 SB

PB BCPB

0.915 0.934 0.953 0.954 0.957 0.958 0.961 0.961 0.928 0.941 0.961 0.961 0.962 0.963 0.964 0.965 0.935 0.947 0.965 0.965 0.965 0.966 0.967 0.966 0.903 0.923 0.946 0.945 0.952 0.951 0.955 0.959

0.855 0.868 0.873 0.877 0.881 0.884 0.886 0.890 0.852 0.866 0.871 0.876 0.880 0.883 0.886 0.889 0.849 0.864 0.870 0.875 0.879 0.883 0.886 0.889 0.859 0.870 0.874 0.878 0.881 0.884 0.887 0.890

 0.801 SB PB BCPB

0.934 0.955 0.959 0.964 0.965 0.966 0.968 0.972 0.943 0.961 0.966 0.969 0.969 0.969 0.973 0.974 0.950 0.966 0.969 0.971 0.972 0.972 0.973 0.975 0.921 0.945 0.952 0.959 0.96 0.963 0.965 0.972

0.724 0.745 0.755 0.760 0.768 0.772 0.777 0.782 0.720 0.743 0.753 0.759 0.767 0.772 0.777 0.782 0.716 0.741 0.752 0.758 0.766 0.771 0.776 0.782 0.728 0.747 0.756 0.761 0.768 0.773 0.777 0.783

0.85 SB

PB BCPB0

0.934 0.949 0.957 0.959 0.960 0.963 0.968 0.970 0.942 0.956 0.963 0.963 0.964 0.966 0.971 0.972 0.949 0.959 0.965 0.965 0.967 0.969 0.973 0.973 0.919 0.942 0.954 0.954 0.955 0.960 0.965 0.968

0.791 0.808 0.815 0.820 0.826 0.829 0.832 0.836 0.787 0.806 0.814 0.819 0.825 0.828 0.832 0.836 0.784 0.805 0.813 0.818 0.824 0.828 0.832 0.836 0.794 0.810 0.816 0.821 0.826 0.829 0.833 0.836

0.90 SB

PB BCPB

0.931 0.945 0.955 0.957 0.964 0.964 0.966 0.969 0.940 0.953 0.961 0.961 0.970 0.967 0.969 0.972 0.947 0.959 0.965 0.965 0.974 0.970 0.972 0.974 0.918 0.937 0.946 0.951 0.959 0.961 0.962 0.967

0.861 0.872 0.877 0.880 0.883 0.886 0.888 0.891 0.859 0.871 0.876 0.879 0.883 0.885 0.888 0.891 0.857 0.870 0.875 0.878 0.882 0.885 0.888 0.891 0.864 0.874 0.878 0.880 0.884 0.886 0.889 0.891

在文檔中製程能力指標Yq/Y複式抽樣之信賴下限 (頁 49-86)