世代和年代生育率、死亡率模型的比較 - 政大學術集成
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(2) 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i Un. v. 100. 6.
(3) 89. 1.68. 98. 1.03. 99. 0.90. (Total Fertility Rate) (Completed Cohort Fertility Rate). 立. 政 治 大. ‧ 國. Gamma. Gompertz. (Principle Component. ‧. io. sit. y. Nat. n. al. er. Analysis). 學. 35. (Extrapolation). Ch. engchi. i Un. v. Gamma. Gamma Lee-Carter. i. Gompertz.
(4) Abstract. Taiwan’s fertility rates have been declining radically in recent years, much faster than most countries in the world. For example, the total fertility rate (TFR) is 1.68 in 2000, 1.03 in 2009, and even reduces to 0.90 in 2010. Therefore, one of the top priorities for Taiwan government policies is to enhance the willingness of having children. Due to the data availability, the TFR is used more often, although the completed cohort fertility rate (CFR) is a more reasonable measurement. However, previous studies showed that the TFR is likely to be influenced by the deferring (i.e.,. 政 治 大. tempo effect) of childbearing and produces misleading results. In order to measure the effect of deferring childbearing, this study focuses on exploring the difference of. 立. measures in the view of cohort and period (especially the CFR vs. TFR) and evaluates. ‧ 國. 學. which fertility and mortality model is more appropriate for Taiwan. Because there are fewer complete cohort fertility data, we use extrapolation to. ‧. make up the higher age-group fertility data (such as aged 35 and above). We consider. sit. y. Nat. four fertility models in this study, including Gamma model, Gompertz model, principal component analysis, and individual group estimation. We use the data from. io. n. al. er. Taiwan, Japan, France and United State data to evaluate these fertility models. The. i Un. v. results indicate that the parametric models (Gamma and Gompertz) have the worst. Ch. engchi. performance, probably due to the rapid change of fertility behaviors. In addition, similar to evaluating the fertility models, we compare the performance of frequently used mortality models using the cohort and period mortality data. The result shows that using cohort data to estimate fertility and mortality is better than period data. Also individual group estimation is the best model to fit fertility; the better models to fit mortality are Gamma model, principle component analysis and individual group estimation. Key Words: Completed Cohort Fertility Rate, Gamma function, Gompertz function, principle component analysis, Lee-Carter Model.. ii.
(5) ............................................................................................................... 1 .................................................................................................... 1 .................................................................................................... 1 ....................................................................................................... 4 Gamma. .............................................................................................. 4. Gompertz. ........................................................................................... 4. 政 治 大. ................................................................................................ 5. 立. .......................................................................................... 6. ‧ 國. 學. Lee-Carter. ............................................................................ 6. ............................................................................... 8. ‧. .................................................................................... 8. .......................................................................... 15. er. io. sit. y. Nat. .................................................................................. 13. n. 20 a......................................................................................... v i l C n h .............................................................................. 20 engchi U. TFR. CFR. ........................................................................ 23 .......................................................................... 26 .................................................................................. 27. ................................................................................................. 29 ...................................................................................................................... 32 .............................................................................................................................. 35. iii.
(6) 3-1 TFR. ....................................................................... 18. 3-2. TFR. TFR. CFR. .................... 19. 4-1. ....................................................... 21. 4-2. ....................................................... 22. 4-3. MAPE ........................... 24. 4-4. MAPE ....................................... 28. 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. iv. i Un. v.
(7) 1-1. ......................................................... 2. 3-1. ......................................................................... 9. 3-2. ......................................................................... 9. 3-3. ....................................................................... 10. 3-4. ....................................................................... 10 CFR. ..................................................................................... 11. 3-6. 立. 3-7. 4-2. ............................................................................. 17. y. sit. TFR. al. n. 4-1 15~39. io. 3-12. .............................................................. 17. Nat. 3-11 TFR. ................................................ 16. ‧. 3-10. ................................................... 15. ‧ 國. 3-9. ................................................... 14. 學. 3-8. 治 ........................................................................... 12 政 大. TFR............................................ 18. 15~49. Ch. er. 3-5 TFR. v ni. ........................ 20. U e n g c h i 2005~2009. TFR. ...... 23. 1981~1985. CFR. ..... 25. 4-3 4-4. (MAPE) ......... 27. 5-1. ....................................................................... 31. 5-2. ....................................................................... 31. v.
(8) 89. 1.68. 0.901. 89. 98. 1.03. 31. 99. 99. 17. 10. 15~64. 2010. 2060 14%. (ageing). 立. 政 治 (aged) 大. ‧. ‧ 國. 學. n. al. er. io. sit. y. Nat 1-1. 2017. Ch. engchi. i Un. v. 1970. (Total Fertility Rate TFR) Tempo. (Completed Cohort Fertility Rate 1-1 1. (http://www.ris.gov.tw/). 1. 2007. CFR).
(9) TFR. CFR. CFR. TFR 1976. TFR. 2000. CFR. CFR 15~49. TFR. 1-1. CFR. 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i Un. v. 1-1. TFR TFR 2. CFR.
(10) , 2002. , 2003. CFR. (Goldstein, 2010. Cheng and Lin, 2010). TFR. CFR , 2006 , 2005. (Diffusion Model). Bongaarts and Feeney, 1998. 立. , 2006. Gompertz. ‧ 國. 學 ‧. Lee-Carter. n. al. er. io. sit. y. Nat (Cross Validation). CFR. 政 治 Gamma 大. Ch. engchi. 3. i Un. v.
(11) Gamma. Gompertz. Lee-Carter. Lee-Carter. Gamma Gamma. 治 政 β 大e f ( x) = x e = Kx Γ ( ) α 立. f ( x). β. α −1 − β x. x. βt. y. sit. ln f ( xt ) = ln K t + (α t − 1) ln xt − β t xt + ε t. al. n. αt −1. (Scale Parameter). er. io. ln K t. Ch. engchi 2. (1). Gompertz. 2. εt. α. ‧. Nat εt. βα Γ(α ). K. (Shape Parameter). t. α −1 − β x. 學. ‧ 國. α. σ2. 0. 4. i Un. v. (Ordinary Least Square) t. (1).
(12) Gompertz. Booth(1984) Goldstein(2010). Gompertz. Gompertz Gompertz. Gompertz. F ( x) = KAB F(x). 2002. x. 0 < A < 1. K. 立. A. B. 政 治 大. ‧ 國. 學. t. (2). (2). sit. y. ‧. Nat. (Principle Component Analysis. io. n. al. PCA). er. F. x. F ( x) } = − ln(− ln A) + (− ln B) x = a + bx F. − ln{− ln a b. 0 < B < 1. Ch. engchi. i Un. v. 15~49 loading score. 5.
(13) Gamma Gompertz Gamma. Gompertz 15~49 t. , 2002. 立. 政 治 大. ‧ 國. 學. Lee-Carter Lee-Carter. ‧ y. Nat. Lee-Carter. io. n. al. t. t. x. ln( mx ,t ) = ax + bx kt + ε x ,t. Ch. engchi. sit. Lee-Carter. m x ,t. (2002). er. Wilmoth(1996). Lee and Carter(1992). i n U a b x. v. x. ε x ,t. kt. x SVD(Singular Value Decomposition. ax bx kt. SVD). SVD. 1. ax. 40~84. ln( mx ,t ). ax. 6. 9.
(14) 2. bx. kt. ln( mx ,t ) − ax. ln( mx ,t ) − ax. bx. kt. ln( mx ,t ) − ax. kt kt. 3.. kt. 立. ax. bx. kt. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 7. i Un. v. Lee-Carter.
(15) 15. 49. 0. 99. (Age-specific Fertility Rate ASFR). 政 治 大. (TFR). 立. x =ζ. x =ζ. x+n. n. 5. Bx ( z ). z. x. η. y. z. x. n. al. Fx ( z ). n. x+n. Ch. 3-1. engchi. i Un. 1949. 1. v. 1960 1980. 20-34 20-29. 30-34 2000. 30-34 2009. 20-24. 30-34. 20-24 25-29. 25-29. 1.0. 8. ζ 15. er. n. io. 49. Bx ( z ) n Fx ( z ). n. sit. x. Nat. x+n. η. ‧. z. f x ( z). η. TFR( z ) = n∑ n f x ( z ) = n∑. 學. n. ‧ 國. Brown(1997).
(16) 3-2 1960. 2009 2-2. 20-29. 30-39. 1980. 20-24. 2009. 立. 政 治 大. 15-19 20-24 25-29. 學. 30-34 35-39. ‧. 40-44. 2009 2004 1999 1994 1989 1984 1979 1974 1969 1964 1959 1954 1949. ‧ 國. 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0. Nat. er. io. sit. y. 45-49. 3-1. n. al. Ch. engchi. i Un. 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0. v. 15-19 20-24 25-29 30-34 35-39 2009 2006 2003 2000 1997 1994 1991 1988 1985 1982 1979 1976 1973 1970 1967 1964 1961 1958 1955 1952 1949. 3-2. 9. 40-44 45-49. 30-34 25-29.
(17) 1970. 1980. 3-3. 30-39. 25-29. 20-24. 1980. 30-34. 2009. 25-29 30-34 2.0. 立. 政 治 大. 20-24 25-29 30-34. 學. 35-39 40-44 45-49. sit. y. ‧. io. 3-3. n. al. er. Nat 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0. 15-19. 2009 2004 1999 1994 1989 1984 1979 1974 1969 1964 1959 1954 1949. ‧ 國. 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0. Ch. engchi. i Un. v. 15-19 20-24 25-29 30-34 35-39 40-44 2009 2004 1999 1994 1989 1984 1979 1974 1969 1964 1959 1954 1949. 3-4. 10. 45-49.
(18) 3-4 30-39. 1970. 20-24 1970. 2.0. 30-39. 3-1. 3-4. 20-29 30-39 30-39. 30-34. 25-29. 政 治 大. 立. 25-29. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 3-5 TFR. i Un. CFR. (TFR). 15-49. (CFR). 15-49 CFR. 35 11. v. 30-34.
(19) 3-5. 政 治 大. 立. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i Un. v. 3-6. 1960 3-6 15-24. 12. 15.
(20) 15-39. 1960. 政 治 大. 立. ‧. ‧ 國. 學. 3-8. y. Nat. 40. 2009. n. er. io. 1960. al. 84. sit. 3-7. && (2010) Hans Lundstrom. Ch. engchi. 1910. i Un. v. 1925. 0 Human Mortality Database. 1996 2009. 85. 81. 80 2008 80. 80. 13.
(21) (ageing). (aged). 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 3-7. 14. i Un. v.
(22) 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. 3-8. Ch. (Quantum). engchi. i Un. v. (Tempo). (TFR) (CFR). TFR. Ryder(1960, 1964). CFR. (1990). Ryder Bongaarts and Feeney(1998) 15. Norman.
(23) TFR. CFR. Bongaarts and Feeney. Goldstein and Cassidy. (2010) 1950. 1980. 2010 30. TFR. 3-9. 20. 10. 30 1950 1980. 1980. 2010. 3-10. 3-9. 30 26. 立. 30. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 3-9. 16. i Un. v. 26.
(24) 3-10. 立. 30. TFR. 20. TFR. 3-1. 30. 20. 10. TFR. io. 14.45% 20.08% 20.86% TFR. n. al. CFR. Ch. engchi. 3-11 TFR 17. sit. 19. er. 25. CFR. y. 13.93% 20.26% 29.31% TFR. Nat. 31. CFR. ‧. TFR. 10. 學. 3-11. 2.0. ‧ 國. TFR. 政 治 大. i Un. v. 34. 27. 22.
(25) 3-1 TFR 30. 20. 10. TFR. 34 2.29 14.45%. 27 2.40 20.08%. 22 2.53 20.86%. TFR. 31 1.72 13.93%. 25 1.59 20.26%. 19 1.41 29.31%. 1980. 立19 TFR. 3-12. 1980 TFR. TFR. TFR. sit. io. n. al. TFR. CFR 1985. 0.5. Ch. engchi. 3-12. i Un. TFR. 18. CFR. TFR. er. TFR. 1992. Nat. 1984. 3-2. 1980 TFR. y. TFR. CFR. ‧. ‧ 國. TFR. 29.31% TFR. 學. 1994. TFR. TFR 政 治 大 1961 1975. 3-1 CFR. 1994. v. TFR. CFR TFR.
(26) 3-2. TFR. adj-TFR adj-TFR ─ TFR 3.25 0.74 3.17 0.72 3.00 0.68 2.81 0.64 2.66 0.60 2.43 0.55 2.17 0.49 2.20 0.50 2.40 0.54 2.17 0.49 2.34 0.53 2.22 0.50 2.24 0.51 2.28 0.52 2.27 0.51. TFR 2.52 2.46 2.32 2.17 2.06 1.88 1.68 1.70 1.86 1.68 1.81 1.72 1.73 1.76 1.76. ‧ 國. 立. CFR. CFR 3.09 2.97 2.85 2.76 2.68 2.61 2.56 2.51 2.47 2.42 2.38 2.33 2.29 2.24 2.20. 政 治 大. 學. Period 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994. TFR. ‧. TFR. Cohort 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975. al. (TFR). Ch. 1.03. engchi. TFR. sit. 2060. er. 2010. n. TFR. io. 2009. y. Nat. TFR. i Un. v. TFR. 19.
(27) TFR Gamma. CFR Gompertz Lee-Carter. 政 治 大. 立. ‧ 國. 學. (Age-specific Fertility Rate ASFR). (Cohort Age-specific Fertility Rate CAFR). ‧. 35. 15. Nat. y. 49. n. al. ~2009. er. io. 1949. sit. 1960~2009. 1960~2009. Ch. engchi. 4-1 15~39. 15~49. 20. i Un. v.
(28) 40. 4-1. TFR. 95%. 15~39. TFR. 15~49. CFR. 15~39 4-1 ( ). ( ). 1960~2004 1949~1980. 2005~2009 1981~1985. 1960~2004 1960~1980. 2005~2009 1981~1985. 1960~2004 1949~1980. 2005~2009 1981~1985. 1949~1980. 2005~2009 1981~1985. 政 治 大 1960~2004. 立. ‧ 國. 學. ‧. http://www.mhlw.go.jp/ http://www.humanfertility.org/cgi-bin/main.php http://www.humanfertility.org/cgi-bin/main.php. y. Nat. TFR. n. al. 1960~2004. 2005~2009. Ch. 2009 1949 1981. 15. 15 1960. (Testing). er. io. sit. (Training). 1949~2004. engchi 1980. 1985. i Un. v. 2005. 15. 15. 1980. 1981. 1985. 4-1. Gamma Gompertz. Lee-Carter 21.
(29) 40. 84 1910. 40. 16. 40. 4-2 4-2 ( ). 立. 1960~2004 1910~1920 1960~2004 1910~1920 1960~2004 1910~1920 1960~2004 1910~1920. 政 治 大. ‧ 國. Mean Absolute Percentage Error. ‧. Root Mean Square Percentage Error. n. er. io. MAPE. sit. y. Nat Yˆi. RMSPE. ˆ 1 n Yi − Yi MAPE = ∑ ×100% n i =1 Yi a. iv l C n h e n g c hˆ i U Y −Y 1. RMSPE =. Yi. 2005~2009 1921~1925 2005~2009 1921~1925 2005~2009 1921~1925 2005~2009 1921~1925. 學. MAPE. ( ). 2. n. n. ∑ i =1. i. Yi. i. × 100% . Yi. RMSPE. MAPE RMSPE. MAPE. MAPE. Lewis(1982). <10%. MAPE. 10%~20%. 22. 20%~50%. >50%. 1925.
(30) 1.3. TFR. Gamma. Gompertz. 1.9. PCA. Gamma Gompertz. 2009. y 2007. PCA. TFR. n. er. io. sit. 2006. 2005. 2008. ‧. 1.7. 2005~2009. CFR. 2009. 2. 1.8. PCA. al. 2008. 2007. 2005. TFR. Gamma. Nat TFR. 2006. 1.0. 政 治 2.2大 2.1. 立. 4-2. Gompertz. 1.1. PCA. 2.3 2.2 2.1 2 1.9 1.8 1.7 1.6. Gamma. 1.2. Gompertz. ‧ 國. TFR. 1.4. 學. TFR. 1.5. 1.2 1.1 1 0.9 0.8 0.7 0.6. Ch. engchi. i Un. v. 4-3 MAPE TFR TFR. Gamma 4-2. Gamma. 4-2. Gompertz Gompertz. Gompertz MAPE 1. 23. 8.
(31) TFR. Gamma. Gompertz. Gamma. Gompertz. MAPE. 4-3. MAPE (. Gompertz. 8.63. 4.37. 治2.97 0.12 政 大 5.14 7.55. 2.44. 1.14. 1.78. 0.94. 3.45. 2.62. 9.34. 5.50. 8.40. 1.45. 5.57. 5.96. 1.60. 5.37. 1.80 5.14. 學. 1.64. 4.03. 9.87. 1.52. 1.73. 2.26. 1.73. 0.56. 0.98. 1.28. ‧. ‧ 國. 立. Gamma. n. a l 15 Ch. er. io. sit. y. Nat. 32. 1949 1960. 15. %). 1980. 1980. i Un. 15. e15n g c h i. v. 21. Gamma. 4-3. Gompertz 4-3. Gamma. MAPE Gamma. 24.
(32) 2 1.8. CFR. CFR. 1.9 Gamma. 1.7 Gompertz. 1.6 1.5. 1.8 1.7 1.6 1.5 1.4 1.3 1.2. Gamma Gompertz PCA. 2.2. 2.3 2.2 2.1 2 1.9 1.8 1.7 1.6. CFR. 政 治 2.1大 2 立Gamma 1.9. Gompertz. 1981~1985. PCA. 1985. 1984. 1983. 1981. ‧. sit. y. CFR. n. al. er. io. TFR. 1982. 1.7. Nat. 4-3. 1.8. PCA. Gamma. 學. Gompertz. ‧ 國. CFR. PCA. MAPE. Ch. engchi. i Un. 1.14% 2.62% 1.73%. MAPE. v. 4-2. 1.64% MAPE. Gompertz. Gamma. Gamma MAPE. Gompertz MAPE MAPE MAPE MAPE. Gompertz 25.
(33) Gamma. MAPE MAPE MAPE. MAPE. Gamma. MAPE. MAPE. MAPE. MAPE. 立. MAPE 政 治 大 1 8. 30~34. 35~39. MAPE. MAPE MAPE. y. Gompertz 10%. 4-4. a l Gamma 35~39 i v n Ch U i e n gMAPE 35~39 h c n. 15~19 MAPE 15~19. 25~39. 40%. sit. io. MAPE. MAPE. er. Nat. 25~29. MAPE. 50% Gamma. ‧. 15~19. ‧ 國. 20~24. 學. Gompertz. MAPE. MAPE. 26. 20% 10%. MAPE. 30%.
(34) 60 Gamma. 40 30. Gamma. 40. Gompertz. 20 PCA. 10. 50. 30. Gompertz. 20 PCA. 10. 立. 30-34. 35-39. 2006. ‧. n. al. er. io. sit. y. Nat. 4-4. (MAPE). 政 治 大. 學. Gompertz. 25-29. 15-19. 4-4. 20-24. 0. 0. ‧ 國. MAPE(. ). 50. MAPE(. ). 60. Ch. engchi. MAPE MAPE. 9. i Un. v. 16. Gompertz. Gamma. Lee-Carter. MAPE 12%. MAPE MAPE Gamma. Gompertz. MAPE Gompertz. MAPE 27.
(35) MAPE Gamma. MAPE. Gamma MAPE. 立. 4-4. 政 治 大 MAPE. (. %). 3.85. 41.94. 4.36. 6.73. 39.85. 4.42. a l3.09 10.75 Ch. 39.86. 2.04. io. n. 6.43. y. 9.25. sit. 46.12. er. 5.86. Nat. Gompertz. ‧. ‧ 國. 學 Lee-Carter. Gamma. iv 35.10 5.54 n e n35.73 g c h i U2.86. 8.93. 6.91. 4.23. 5.96. 11.24. 4.73. 2.73. 3.15. 5.41. 4.16. 3.39. 3.90. 3.04. 41.09. 4.74. 7.63. 3.53. 2.45. 38.65. 2.84. 3.29. 4.06. 28.
(36) (TFR) (CFR). 2003. 政 治 大 MAPE. 學. ‧ 國. 立 Gamma. 35. ‧. io. sit. y. Nat MAPE. n. al. er. 35~39. 25~29. Ch. engchi. 2009. 30~34. i Un 5-1. v. 35. 5-2 (Tempo) TFR. TFR 2009. TFR. 1.03. TFR MAPE Gamma. Lee-Carter 29.
(37) Gompertz Gompertz. Gamma Lee-Carter. 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i Un. v. (Quantum) (Tempo). 2010. (TFR). 1.0 2005 CFR TFR. Bongaarts and Feeney(1998) CFR. 30.
(38) 台台台台台. 1.0 0.0. 0.5. 五年五五五五. 1.5. 1960 1970 1980 1990 2000 2004 2007 2009. 20. 25. 30. 35. 40. 45. 政 治 大 年年. 5-1. 學. ‧ 國. 立. 日日台台台. y. sit er. 0.6. al. Ch. engchi. i Un. v. 0.0. 0.2. n. 0.4. io. 五年五五五五. Nat. 0.8. ‧. 1.0. 1960 1970 1980 1990 2000 2004 2007 2009. 20. 25. 30. 35 年年. 5-2. 31. 40. 45.
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(41) Ryder, N. B. (1964),. The Process of Demographic Transition”, Demography, 1(1),. 74-82. Statistics Japan, http://www.stat.go.jp Statistics France, http://www.humanfertility.org/cgi-bin/main.php Statistics United States, http://www.humanfertility.org/cgi-bin/main.php Wilmoth, J. R. (1996),. Mortality projections for Japan: a comparison of four. methods”, Health and Mortality Among Elderly Populations, 266-287. 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 34. i Un. v.
(42) 1. (MAPE). (%). Gamma. Gompertz. 15~19. 17.23. 30.99. 35.17. 22.56. 20~24. 15.27. 52.65. 7.77. 25.06. 25~29. 5.36. 8.94. 12.45. 7.33. 30~34. 25.59. 36.07. 7.19. 12.59. 35~39. 9.05. 25.11. 30.45. 15.35. 2 Gamma 15~19. 立. 6.94. 25~29. 4.20. 29.93. 12.55. 8.34. 6.18. 6.94. 3.59. 4.41. 12.54. 27.43. 10.23. 1.73. 35~39. 8.05. 23.72. 5.96. sit. (MAPE). n. al. 15~19. 14.69. 20~24. 20.21. 25~29. er. io Gamma. 1.40. y. Nat 3. ‧. 30~34. 7.07. 學. 20~24. (%). 43.33. ‧ 國. 3.19. 政 治 大(MAPE) Gompertz. Gompertz iv n C h 44.22 e n g c h i U 2.37. (%). 1.88. 35.36. 7.52. 9.30. 5.46. 5.48. 8.11. 1.55. 30~34. 4.17. 26.18. 4.25. 3.53. 35~39. 7.45. 27.88. 7.26. 5.79. 35.
(43) 4. (MAPE). (%). Gamma. Gompertz. 15~19. 2.81. 24.50. 8.79. 2.78. 20~24. 3.12. 17.66. 4.44. 3.11. 25~29. 6.15. 8.76. 3.78. 1.59. 30~34. 5.08. 25.19. 7.36. 2.06. 35~39. 2.68. 32.09. 2.48. 1.52. 5. (MAPE) Gamma. Gompertz. 15~19. 2.11. 36.92. 20~24. 4.97. 25~29. 4.68. 30~34. 3.64. 35~39. 11.91. 治 7.68 政26.17 大17.61 2.81. 6.62 1.17. 22.85. 8.16. 3.18. 14.57. 21.57. 4.06. ‧. ‧ 國. 32.12. 學. 6. 立. 38.57. (%). (MAPE). (%). 15~19. 13.18. 34.73. 5.21. 20~24. 21.32. 35.40. 9.82. 1.80. 25~29. 6.33. 1.27. 8.80. 2.50. 30~34. 6.18. iv n9.01. 1.19. 35~39. 7.87. C h 24.13 e29.54 n g c h i U 5.50. n. 7. sit. er. io. al. y. Gompertz. Nat. Gamma. (MAPE). 12.60. 1.61. (%). Gamma. Gompertz. 15~19. 9.20. 24.98. 33.78. 12.93. 20~24. 2.61. 21.94. 8.67. 1.67. 25~29. 2.14. 2.59. 6.04. 2.11. 30~34. 3.14. 22.23. 6.92. 2.59. 35~39. 3.99. 29.33. 21.58. 1.64. 36.
(44) 8. (MAPE). (%). Gamma. Gompertz. 15~19. 6.21. 16.70. 0.62. 9.35. 20~24. 9.19. 13.61. 4.58. 1.59. 25~29. 1.77. 9.05. 9.87. 3.33. 30~34. 8.13. 24.17. 1.87. 3.78. 35~39. 4.89. 34.24. 8.36. 3.00. 9. (MAPE) Gamma Gompertz. 45-49. 3.87. 50-54. 2.39. 42.63. 55-59. 5.70. 2.61. 6.53. 3.22. 3.15. 71.29. 12.98. 9.50. 6.55. 6.88. 55.44. 10.12. 8.66. 7.59. 8.25. 17.40. 11.30. 13.61. 11.25. 6.42. 25.36. 13.43. 13.70. 10.64. 6.36. 56.63. 14.08. 15.60. 6.39. 6.13. 76.89. 10.29. 4.36. 5.08. n. 10. y. sit. io. al. er. 80-84. Nat. 75-79. 2.60. ‧. 70-74. 8.92. 立. ‧ 國. 65-69. 9.08. 學. 6.76. 60-64. Lee-Carter. 57.25 治1.77 政 12.14 2.79 大. 40-44. (%). Ch. engchi. Gamma Gompertz. v i(MAPE) n U. (%). Lee-Carter. 40-44. 7.92. 41.67. 1.33. 18.75. 8.95. 45-49. 3.94. 10.58. 4.35. 15.35. 4.28. 50-54. 9.19. 27.05. 5.13. 14.97. 1.38. 55-59. 5.38. 49.63. 2.79. 17.20. 4.60. 60-64. 5.06. 50.33. 4.60. 12.39. 5.48. 65-69. 11.00. 20.82. 6.93. 8.65. 4.57. 70-74. 6.81. 22.83. 4.72. 8.26. 7.26. 75-79. 0.79. 56.89. 4.68. 3.21. 4.36. 80-84. 10.45. 78.84. 5.24. 2.36. 1.65. 37.
(45) 11. (MAPE) Gamma Gompertz. (%). Lee-Carter. 40-44. 11.66. 34.32. 12.07. 2.21. 3.83. 45-49. 15.02. 17.23. 2.64. 7.14. 3.33. 50-54. 22.45. 13.98. 4.74. 10.81. 6.01. 55-59. 17.18. 38.15. 3.32. 8.71. 7.87. 60-64. 8.24. 38.52. 1.40. 6.46. 5.91. 65-69. 1.82. 15.05. 5.08. 2.79. 3.30. 70-74. 4.40. 22.60. 6.67. 0.75. 0.83. 75-79. 4.10. 56.88. 6.37. 3.11. 1.72. 80-84. 11.84. 79.20. 7.57. 6.71. 4.68. 立. Gamma Gompertz. 16.76. 5.65. 13.16. 2.39. 16.87. 3.92. 34.43. 4.59. 8.88. 2.24. 61.56. 5.45. 5.17. 2.08. 44.27. 4.59. 6.84. 4.45. 11.60. 4.75. iv n3.50. 4.24. 3.12. 1.86. 2.28. 2.28. io. 60-64. 5.02. al. 3.06. 70-74. 3.90. 75-79. 3.25. 80-84. 1.92. n. 65-69. C24.89 U h e n g c6.81 i h 54.90 4.37 75.49. 4.71. 38. 1.75. y. sit. 55-59. 49.49. Nat. 50-54. 1.28. ‧. 45-49. (%). Lee-Carter. er. 40-44. (MAPE). 學. ‧ 國. 12. 政 治 大. 5.22. 3.66 7.19 2.33. 3.99.
(46) 13. (MAPE) Gamma Gompertz. (%). Lee-Carter. 40-44. 9.63. 55.54. 4.01. 11.46. 7.40. 45-49. 0.40. 9.20. 1.04. 3.74. 1.64. 50-54. 4.05. 42.26. 3.19. 2.62. 1.89. 55-59. 4.07. 60.32. 1.12. 1.64. 1.40. 60-64. 5.49. 47.23. 12.23. 4.52. 6.90. 65-69. 3.61. 9.60. 6.86. 13.71. 8.78. 70-74. 2.81. 26.76. 5.09. 6.86. 4.14. 75-79. 1.59. 54.01. 4.65. 6.67. 4.64. 80-84. 3.00. 72.50. 1.03. 2.45. 1.23. 立. Gamma Gompertz. 4.59. 5.34. 9.30. 1.14. 2.01. 5.94. 33.44. 2.75. 2.16. 0.68. 58.32. 1.16. 0.74. 2.28. 47.94. 0.72. 2.81. 1.74. 13.82. 3.33. iv n3.10. 3.94. 3.01. 2.73. 5.99. 6.02. io. 60-64. 0.76. al. 2.46. 70-74. 1.10. 75-79. 1.77. 80-84. 6.37. n. 65-69. C25.89 U h e n g c0.47 i h 55.18 2.50 76.02. 5.58. 39. 3.54. y. sit. 55-59. 38.87. Nat. 50-54. 1.88. ‧. 45-49. (%). Lee-Carter. er. 40-44. (MAPE). 學. ‧ 國. 14. 政 治 大. 3.96. 1.90 2.08 0.98. 1.64.
(47) 15. (MAPE) Gamma Gompertz. (%). Lee-Carter. 40-44. 3.85. 36.39. 7.51. 9.78. 9.09. 45-49. 9.45. 16.10. 0.87. 2.37. 1.65. 50-54. 10.74. 18.84. 2.41. 3.26. 2.31. 55-59. 4.25. 41.42. 1.10. 1.31. 0.87. 60-64. 3.13. 38.14. 0.60. 1.66. 1.63. 65-69. 10.07. 14.28. 0.91. 1.58. 0.95. 70-74. 7.19. 23.71. 5.50. 5.58. 5.95. 75-79. 1.12. 56.20. 2.22. 3.59. 3.20. 80-84. 8.08. 76.51. 4.63. 5.97. 4.86. 立. Gamma Gompertz. 9.15. 6.91. 14.08. 3.90. 1.49. 1.95. 33.64. 4.27. 7.85. 2.95. 55.31. 4.44. 1.37. 0.59. 37.15. 0.69. 4.85. 3.61. 7.85. 2.56. iv n1.19. 2.57. 1.70. 0.84. 6.26. 5.53. io. 60-64. 0.32. al. 2.47. 70-74. 1.95. 75-79. 0.75. 80-84. 2.50. n. 65-69. C26.57 U h e n g c2.88 i h 55.31 1.75 73.40. 4.73. 40. 6.38. y. sit. 55-59. 44.58. Nat. 50-54. 1.97. ‧. 45-49. (%). Lee-Carter. er. 40-44. (MAPE). 學. ‧ 國. 16. 政 治 大. 2.66. 1.81 6.14 1.24. 1.47.
(48) 1. 60. ). 50 40 MAPE(. Gamma 30. Gompertz. 20. PCA. 10 0 15-19. 20-24. 立. 30-34 35-39 政 治 大. 25-29. ‧ 國. 學. 2. MAPE(. y. sit. n. al. er. ). io. 40. ‧. 50. Nat. 60. 30 20. Ch. engchi U. 10 0 15-19. 20-24. 25-29. 30-34. 41. 35-39. v ni. Gamma Gompertz PCA.
(49) 3. 60. ). 50 40 MAPE(. Gamma 30. Gompertz. 20. PCA. 10 0 15-19. 20-24. 立. 30-34 35-39 政 治 大. 25-29. ‧ 國. 學. 4. MAPE(. y. sit. n. al. er. ). io. 40. ‧. 50. Nat. 60. 30 20. Ch. engchi U. 10 0 15-19. 20-24. 25-29. 30-34. 42. 35-39. v ni. Gamma Gompertz PCA.
(50) 5. 60. ). 50 40 MAPE(. Gamma 30. Gompertz. 20. PCA. 10 0 15-19. 20-24. 立. 30-34 35-39 政 治 大. 25-29. ‧ 國. 學. 6. MAPE(. y. sit. n. al. er. ). io. 40. ‧. 50. Nat. 60. 30 20. Ch. engchi U. 10 0 15-19. 20-24. 25-29. 30-34. 43. 35-39. v ni. Gamma Gompertz PCA.
(51) MAPE(. ). 7. 90 80 70 60 50 40 30 20 10 0. Gamma Gompertz. Lee-Carter. 立. 政 治 大. ‧ 國. 學. 8. MAPE(. 30 20. y. sit. al. n. 40. io. 50. er. ). 60. ‧. 70. Nat. 80. Ch. engchi. 10 0. 44. i Un. v. Gamma Gompertz. Lee-Carter.
(52) MAPE(. ). 9. 90 80 70 60 50 40 30 20 10 0. Gamma Gompertz. Lee-Carter. 立. 政 治 大. ‧ 國. 學. 10. MAPE(. 30 20. y. sit. al. n. 40. io. 50. er. ). 60. ‧. 70. Nat. 80. Ch. engchi. 10 0. 45. i Un. v. Gamma Gompertz. Lee-Carter.
(53) MAPE(. ). 11. 90 80 70 60 50 40 30 20 10 0. Gamma Gompertz. Lee-Carter. 立. 政 治 大. ‧ 國. 學. 12. MAPE(. 30 20. y. sit. al. n. 40. io. 50. er. ). 60. ‧. 70. Nat. 80. Ch. engchi. 10 0. 46. i Un. v. Gamma Gompertz. Lee-Carter.
(54) MAPE(. ). 13. 90 80 70 60 50 40 30 20 10 0. Gamma Gompertz. Lee-Carter. 立. 政 治 大. ‧ 國. 學. 14. MAPE(. 30 20. y. sit. al. n. 40. io. 50. er. ). 60. ‧. 70. Nat. 80. Ch. engchi. 10 0. 47. i Un. v. Gamma Gompertz. Lee-Carter.
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