混合偏斜t分佈及其應用

Abstract

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.