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系統識別號 U0026-0812200911070823
論文名稱(中文) 極值分配中參數估計之研究
論文名稱(英文) The Study of Parameter Estimation in Extreme Value Distributions
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 92
學期 2
出版年 93
研究生(中文) 陳佳妏
研究生(英文) Chia-Wen Chen
電子信箱 r2691107@mail.ncku.edu.tw
學號 r2691107
學位類別 碩士
語文別 英文
論文頁數 77頁
口試委員 口試委員-潘浙楠
指導教授-路繼先
口試委員-高正雄
中文關鍵字 起始值  門檻值的決定  最大概似估計量 
英文關鍵字 Initial value  Maximum Likelihood Estimation  Threshold Detemination 
學科別分類
中文摘要   在廣義極值分配最大概似估計量的估計中, 由於起始值的決定並非容易, 於是我們針對目前現有的方法進行探討, 提供一套合理且可行的方法, 建立最大概似估計值搜尋的起始值.
  在廣義柏拉圖分配關於門檻值決定的部分, 我們以簡單的方法建立門檻值搜尋的區間.且我們將整個決定門檻值的過程程式化, 自動化.另外我們建立一套明清楚的法則以共最大概似估計量的搜尋.
英文摘要   In the maximum likelihood estimation of the parameters of generalized extreme distribution, the selecting initial values is not a trial task, we study the current available approach and propose an alternative way to establish a reasonable and feasible initial values. As for the determination of the threshold in the generalized Pareto distribution, we propose a simple way to set up the nterval for searching threshold, along with programing the procedure of determining an appropriate threshold and providing a clear-out rule for determining threshold value.
論文目次 Contents
1 Introduction 7
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Extreme Value Models 9
2.1 Block maxima model . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Threshold Excess Model . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Max Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Relationship Between GEV and GPD . . . . . . . . . . . . . . . . . . 15
2.5 N-Year Return Level . . . . . . . . . . . . . . . . . . . . . . . . .16
2.5.1 Generalized Extreme Value Distribution . . . . . . . . . . . . . ..17
2.5.2 Generalized Pareto Distribution . . . . . . . . . . . . . . . . . .18
3 Estimation of Generalized Extreme Value Distribution 20
3.1 General Considerations . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 ML Estimates for Generalized Extreme Value Distribution . . . . . . .21
3.3 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4 Searching ML Estimates for Generalized Extreme Value Distribution 23
3.4.1 What Happened to The 10th Dataset . . . . . . . . . . . . . . . . .25
3.4.2 Solve The Problem . . . . . . . . . . . . . . . . . . . . . . . . .26
3.4.3 Further Examine The Change . . . . . . . . . . . . . . . . . . . . 29
3.5 Possible Modication . . . . . . . . . . . . . . . . . . . . . . . . 32
4 Estimation of the Generalized Pareto Distribution 34
4.1 Graphical Approach for the Choice of Threshold . . . . . . . . . . . 35
4.1.1 Mean Residual Life Plot . . . . . . . . . . . . . . . . . . . . . .35
4.1.2 Stability Plot . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Goodness-of-t Tests Approach . . . . . . . . . . . . . . . . . . . .39
4.2.1 Estimation of Parameters . . . . . . . . . . . . . . . . . . . . . 39
4.2.2 Goodness-of-t Tests . . . . . . . . . . . . . . . . . . . . . . . 40
4.3 Comment on The Current Approach . . . . . . . . . . . . . . . . . . .41
4.4 Modication and Improvement . . . . . . . . . . . . . . . . . . . . .43
4.4.1 Searching for Maximum Likelihood Estimates . . . . . . . . . .. . .44
4.4.2 Improvement for Calculational Convenience . . . . . . . . . . . . .45
4.4.3 The Modication of Rules for Search . . . . . . . . . . . . . . . .47
4.5 Revisit of Wheaton River data . . . . . . . . . . . . . . . . . . . .49
5 Further Result 54
5.1 Revisit the Simulated Datasets . . . . . . . . . . . . . . . . . . . 54
5.1.1 Initial Value Interval . . . . . . . . . . . . . . . . . . . . . . 54
5.1.2 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . 55
5.2 Examine Return Level . . . . . . . . . . . . . . . . . . . . . . . . 56
References 63
Appendix ML Estimates for GEV 65
Appendix ML Estimates for GPD 69
Appendix R functions 73
參考文獻 Choulakian, M. A., and Stephens, V. (2001), "Goodness-of- t tests for the gener-
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Davison, A. C., and Smith, R. L. (1990), "Models for exceedances over high thresholds (with discussion)." Journal of the Royal Statistical Society, 52, 393-442.
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