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研究生:周照偉
研究生(外文):Chao-Wei Chou
論文名稱:關於Gamma分佈及相關問題之研究
論文名稱(外文):A Study of Gamma Distributions and Some Related Works
指導教授:黃文璋黃文璋引用關係
指導教授(外文):Wen-Jang Huang
學位類別:博士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:115
中文關鍵詞:gamma分佈參數Laplace轉換均方誤差反高斯分佈常數迴歸廣義的反高斯分佈測度轉換動差法刻劃beta分佈二維gamma分佈
外文關鍵詞:renewal process.characterizationconstancy of regressiongamma distributionmean squared errorpower of hypothesis testingLaplace transformmethod of momentsgeneralized inverse GaussianPoisson processinverse Gaussian distributionBeta distributionbivariate gamma distributionparameter estimationchange of measure
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分佈刻劃數十年來一直是統計理論的一門重要課題。雖然已經有許多大家熟悉的結果,對於在應用上扮演重要角色的分佈,例如常態及gamma,新的刻劃結果依然相當具有吸引力。在實際應用上,有時我們會猜測觀測到的資料究竟服從什麼分佈,有時會利用刻劃上的特性去推測分佈。本文我們將先探討gamma分佈及利用刻劃上的特性所做的參數估計方法。其次,我們利用電腦模擬來進行一些分析研究。
Characterization of distributions has been an important topic in statistical theory for decades. Although there have been many well known results already developed, it is still of great interest to find new characterizations of commonly used distributions in application, such as normal or gamma distribution. In practice, sometimes we make guesses on the distribution to be fitted to the data observed, sometimes we use the characteristic properties of those distributions to do so. In this paper we will restrict our attention to the characterizations of gamma distribution as well as some related studies on the corresponding parameter estimation based on the characterization properties. Some simulation studies are also given.
Chapter 1: Introduction and Review
Chapter 2: Characterizations of the Gamma Distribution via Conditional Moments
Chapter 3: Characterizations of the Bivariate Gamma distribution
Chapter 4: Characterizations of the Gamma and Generalized Inverse Gaussian distributions
Chapter 5: Characterizations of the Gamma Distribution via Conditional Expectations
Chapter 6: On Parameter Estimation of two Independent Gamma Population With the Same Scale Parameter
Chapter 7: Conclusion
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