臺灣博碩士論文加值系統

我們利用R統計軟體中的 Shiny 套件開發出一套網路介面 OTL (Outlier Testing in Lifetime Data) 來檢測指數、Weibull、對數常態或對數Laplace分配的資料是否有較大或較小離群值。在許多文獻中，虛無假設下區塊或連續檢定程序之檢定統計量的機率分配計算通常是需要用到非常複雜的積分，而且論文所提供的表格數據都是有限的。因此，我們利用Huffer and Lin (2001)的演算法和Iliopoulos and Balakrishnan (2009)的定理讓OTL 介面可以精確地計算出指數與對數 Laplace 模式之檢定統計量的機率分配。而對於 Weibull 與對數常態模式之檢定統計量的機率分配，我們則用 Monte Carlo 模擬方法取得其機率分配之逼近值，並且將所得數據儲存於資料庫，再與 OTL 介面連結以供使用者可以快速取得並做出判斷。使用OTL 介面不但可以節省搜尋表格的時間，也能擴大使用的數據範圍，更可以直接從介面上看到多個檢定統計量離群值檢測之结果，所以OTL 介面對於研究學者、決策者和企業使用者是一個相當有效且方便判斷檢測壽命時間離群值的線上工具。

A web interface, named OTL, is developed to conduct outlier analysis in exponential, Weibull, Lognormal, and Log-Laplace samples online over the Internet through Shiny and R. It is a tool to evaluate the exact or approximate distributions of block and consecutive test statistics on outliers which have been discussed over the years in the literature. Since it allows for identifying outliers without using the classical extensive tables, OTL can be very useful to academics, policy-makers and businesses to compare and understand the results of outlier testing procedures more efficiently.

1 Introduction 1
2 Main Tools for Evaluating the Null Distributions of Test Statistics from Exponential and Laplace Samples 7
2.1 Conditional Independence of Blocked Order Statistics 8
2.2 Recursions 8
3 The OTL User Interface 10
4 Demonstration with Known Data Sets 13
Example 1 13
Block Tests 13
Consecutive Tests 15
Example 2 17
Example 3 18
Example 4 19
5 Concluding Remarks and Possible Future Directions 21
References 22
Appendix A 27
Appendix B 29

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