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研究生:湯健平
研究生(外文):Chien-Ping Tang
論文名稱:應用BBPSO演算法於韋伯分配之區間資料下的參數估計
論文名稱(外文):Applying BBPSO Algorithm to Estimate the Weibull Parameters for Interval Data
指導教授:王福琨王福琨引用關係
指導教授(外文):Fu-kwun Wang
口試委員:王福琨
口試日期:2012-05-30
學位類別:碩士
校院名稱:國立臺灣科技大學
系所名稱:工業管理系
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:50
中文關鍵詞:韋伯分配區間資料最大概似法BBPSO演算法
外文關鍵詞:Weibull distributionInterval dataMaximum likelihood estimationBare bones particle swarm
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本論文主要是在探討雙參數韋伯分配(Weibull Distribution)在區間資料(Interval Data)的情況下,透過最大概似法(Maximum Likelihood Estimator)對其參數進行估計,不同於其它設限資料,區間資料若使用傳統牛頓法不能有效透過概似函數限制式直接求得形狀參數 與尺度參數 的估計值,須使用其他方法來求解。
本文將利用文獻上符合韋伯分配之數筆區間資料,採用BBPSO (Bare Bones Particle Swarm Optimization)方法來求最大概似估計值,再與較廣為使用的中心點近似估計法及現有文獻上使用最大期望演算法(EM Algorithm)加以比較。驗證使用BBPSO所得的概似函數值較優。
In survival analysis, the inspection costs should be concerned. An interval data is widely used in lifetime data analysis. In this article, we present maximum likelihood estimation via Bare Bones Particle Swarm Optimization (BBPSO) algorithm to estimate two parameters of Weibull distribution under interval censored data. This approach can produce more accuracy of the parameter estimation for the Weibull distribution. Additionally, the confidence intervals for the estimators are obtained. Compare to the mid-point method and the EM algorithm, it shows that the maximum likelihood estimates based on BBPSO algorithm perform better.
摘要 I
Abstract II
目錄 III
圖目錄 V
表目錄 VI
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 1
1.3 研究限制 2
1.4 研究架構及流程 2
第二章 文獻探討 4
2.1 韋伯分配 4
2.2 資料型態介紹 7
2.3 參數估計方法 9
2.4參數估計求解方法 15
2.4.1牛頓-羅夫森法 15
2.4.2粒子群演算法 16
2.4.3 最大期望值演算法 19
第三章 研究方法 22
3.1區間設限情況下之參數估計 22
3.2 中心點近似估計法 24
3.3 EM演算法之參數估計 25
3.4 準系統粒子群優化估計 27
第四章 實例分析與驗證 33
第五章 結論 39
5.1 結論 39
5.2未來研究方向: 39
參考文獻 41
附錄一 43
附錄二 45
附錄三 49
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