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研究生:謝宛茹
論文名稱:混合偏斜t分佈及其應用
論文名稱(外文):On the mixture of skew t distributions and its applications
指導教授:李昭勝李昭勝引用關係林宗儀林宗儀引用關係
指導教授(外文):Jack C. LeeTsung I. Lin
學位類別:碩士
校院名稱:國立交通大學
系所名稱:統計學研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:英文
論文頁數:32
中文關鍵詞:EM形式演算法異質性數據最大概似遠離中心的觀察值混合偏斜t分佈截斷性常態分配
外文關鍵詞:EM-type algorithmsHeterogeneity dataMaximum likelihoodOutlying observationsSkew t mixturesTruncated normal
相關次數:
  • 被引用被引用:0
  • 點閱點閱:339
  • 評分評分:
  • 下載下載:33
  • 收藏至我的研究室書目清單書目收藏:0
混合t分佈已被認為是混合常態分佈的一種具穩健性的延伸。近年來, 處理具異質性並牽涉了具不對稱現象的資料問題中, 混合偏斜常態分佈已經被驗證是一種很有效的工具。本文我們提出一種具穩健性的混合偏斜t分佈模型來有效地處理當資料同時具有厚尾、偏斜與多峰型式的現象。除此之外, 混合常態分佈(NORMIX)、混合t 分佈(TMIX)與混合偏斜常態分佈(SNMIX)模型皆可視為本篇論文所提出混合偏斜t分佈(STMIX)的特例。我們建立一些EM-types演算法, 以遞迴的方式去求最大概似估計值。最後, 我們也透過分析一組實例來闡述我們所提出來方法。
A finite mixture model using the Student's t distribution has been recognized as a robust extension of normal mixtures. Recently, a mixture of skew normal distributions has been found to be effective in the treatment of heterogeneous data involving asymmetric behaviors across subclasses. In this article, we propose a robust mixture framework based on the skew t distribution to efficiently deal with heavy-tailedness, extra skewness and multimodality in a wide range of settings. Statistical mixture modeling based on normal, Student's t and skew normal distributions can be viewed as special cases of the skew t mixture model. We present some analytically simple EM-type algorithms for iteratively computing maximum likelihood estimates. The proposed methodology is illustrated by analyzing a real data example.
1. INTRODUCTION 2
2. PRELIMINARIES 4
3. ML ESTIMATION OF THE SKEW t DISTRIBUTION 9
4. THE SKEW t MIXTURE MODEL 13
5. AN ILLUSTRATIVE EXAMPLE 19
6. CONCLUDING REMARKS 23
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