Stacy (1962)首先提出廣義伽瑪分配 (generalized gamma distribution)，此分布被廣泛應用於存活分析 (survival analysis) 以及可靠度 (reliability) 中壽命時間的資料描述。事實上，像是指數分配 (exponential distribution)、韋伯分配 (Weibull distribution) 以及伽瑪分配 (gamma distribution) 都是廣義伽瑪分配的一個特例。
Bologna (1987)提出一個特殊的雙變量廣義伽瑪分配 (bivariate generalized gamma distribution) 可以經由雙變量常態分配 (bivariate normal distribution) 所推得。我們根據他的想法，提出多變量廣義伽瑪分配可以經由多變量常態分配所推得。在過去的研究中，學者們做了許多有關雙變量伽瑪分配。當我們提到雙變量常態分配，由於其分配的型式為唯一的，所以沒人任何人對其分配的型式有疑問。然而，雙變量伽瑪分配卻有很多不同的型式。
在這篇論文中的架構如下。在第二章中，我們介紹並討論雙變量廣義伽瑪分配可以經由雙變量常態分配所推得，接著推導參數估計以及介紹模擬的程序。在第三章中，我們介紹一些對稱以及非對稱的雙變量伽瑪分配，接著拓展到雙變量廣義伽瑪分配，有關參數的估計以及模擬結果也將在此章中討論。在第三章最後，我們建構參數的敏感度分析 (sensitivity analysis)。最後，在第四章中，我們陳述結論以及未來研究方向。 / The generalized gamma distribution was introduced by Stacy (1962). This distribution is useful to describe lifetime data when conducting survival analysis and reliability. In fact, it includes the widely used exponential, Weibull, and gamma distributions as special cases.
Bologna (1987) showed that a special bivariate genenralized gamma distribution can be derived from a bivariate normal distribution. Follow his idea, we show that a multivariate generalized gamma distribution can be derived from a multivariate normal distribution. In the past, researchers spend much time in working on a bivariate gamma distribution. When a bivariate normal distribution is mentioned, no one feels puzzled about its form, since it has only one form. However, there are various forms of bivariate gamma distributions.
In this paper is as following. In Chapter 2, we introduce and discuss the bivariate generalized gamma distribution, then the multivariate generalized gamma distribution is derived. We also develop parameters estimation and simulation procedure. In Chapter 3, we introduce some symmetrical and asymmetrical bivariate gamma distributions, then they are extended to the bivariate generalized gamma distributions. Problems of parameters estimation and simulation results are also discussed in Chapter 3. Besides, sensitivity analyses of parameters estimation are conducted. Finally, we state conclusion and future work in Chapter 4.
| Identifer | oai:union.ndltd.org:CHENGCHI/G0913545023 |
| Creators | 曾奕翔 |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 中文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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