布朗運動及布阿松過程之變異數分析

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蘇筱筑(Xiao-Zhu Su) 查詢紙本館藏

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論文名稱

布朗運動及布阿松過程之變異數分析
(The analysis of variance of Brownian motion and Poisson process.)

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摘要(中)

統計是一門比較的學問，而變異數（analysis of variance）分析為最主要的比較工具。變異數分析的技巧主要是作變異數之分解及自由度（degree of freedom）之分解並以變異數除自由度作統計量對一些分布（如常態分布）的期望值（通常為線性）作概似檢定（likelihood ratio test）。隨機過程數據已日漸重要，但傳統變異數分析似未及於隨機過程。因布朗運動（Brownian motion）及布阿松過程（Poisson process）為許多重要隨機過程之原型，故本文主要目的在將變異數分析之技巧推廣於數據為布朗運動或布阿松過程之情形。

摘要(英)

The classical analysis of variance (ANOVA) has been focused mainly on the mean of the normal distribution. The purpose of this paper is to extend the idea of ANOVA to deal with parameters of Brownian motion and Poisson process.

關鍵字(中)

★ 變異數分析
★ 布阿松過程
★ 布朗運動

關鍵字(英)

★ analysis of variance
★ Brownian motion
★ Poisson process
★ ANOVA

論文目次

第一章簡介…………………………………………………………………1
第二章布朗運動的變異數分析……………………………………………3
第一節同值檢定……………………………………………………………3
第二節行效應檢定…………………………………………………………10
第三節列效應檢定…………………………………………………………30
第四節交互效應檢定………………………………………………………46
第三章布阿松過程的變異數分析…………………………………………63
第一節同值檢定……………………………………………………………63
第二節行效應檢定…………………………………………………………68
第三節列效應檢定…………………………………………………………79
第四章結論…………………………………………………………………90
參考文獻…………………….…………………………………………………98

參考文獻

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指導教授

許玉生(Yu-Sheng Hsu)

審核日期

2004-6-17

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