對 Tsallis 隨機變數的隨機產生器之探討及應用 陳信實、鄧志堅
E-mail: [email protected]
摘 要
Tsallis之分佈由C. Tsallis 於1996年提出來解決退火模擬之問題。此演算法被證明為比一般的退火模擬法；能夠更快的達到 全域的最佳解。但是該函數非常之複雜，無法用一般之隨機變數的產生方法來產生。Tsallis根據R. N. Mantegna(1994)產 生Levy之分佈的演算法，進而導出一個Tsallis隨機變數產生法。但是此方法有著許多問題：當參數 為1.2至1.4時，隨機變數 有可能是虛數。並且當我們用蒙地卡羅(Monte Carlo)模擬法來模擬可能的隨機變數值時，我們發現其直方圖(histogram)與理 論的機率密度函數並沒有完全符合。因此藉由Tsallis所提出之Tsallis隨機變數產生器並不能完全正確的代表理論之分佈，我 們提出一個較佳的產生器更能代表Tsallis隨機變數。
關鍵詞 : Tsallis之分佈 ; 退火模擬法 ; 蒙地卡羅模擬法 ; 隨機變數產生器 目錄
目錄 封面內頁 簽名頁 授權書 ………..………..………. iii 中文摘要 ………
………... iv 英文摘要 ……….…...….. v 誌謝 ………
………. vi 目錄 ………... vii 圖目錄 ………
……….… ix 表目錄 ………...….. xi 第一章 緒論 ……
……….. 1 1.1 研究背景與動機 ……….……….... 1 1.2 研究目的 ………
……….……… 2 1.3 研究範圍與限制 ……….………… 2 1.4 研究流程 ……….…
……… 3 1.5 論文章節架構 ……….……… 6 第二章 文獻探討 ………
……….. 8 2.1 Inversion ……….……..…...………..………..……. 9 2.2 Rejection ……….…..……...………..…..…..…
…. 11 2.3 Composition ….…..……...………..………..…….. 13 2.4 Box Muller’s method …………...….…..……….... 16 2.5 Ingenious Method for Symmetric Stable Variate.. 18 2.6 小結 ……….…....………..……… 19 第三章 研究方 法與流程 ………. 21 3.1 Tsallis隨機變數產生器 ……...………. 21 3.2 Kolmogorov’s statistic檢定…….……….….……. 38 第四章 結論與建議 ……… 44 4.1 結論 ………….…
……….. 44 4.2 建議及後續研究之方向……….……..….. 44 參考文獻 ………
……… 46 附錄一 Algorithm TR……….... 49 附錄二 Chamber stable variate………..….... 51 附錄三 Chambers和Levy之關係式………..……..….... 53 附錄四 C.Tsallis
’ Algorithm ………...………..….... 55 附錄五 Probability distribution of ………..….... 57 參考文獻
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