Statistica Sinica 17(2007), 909-927

FINITE MIXTURE MODELLING USING THE

SKEW NORMAL DISTRIBUTION

Tsung I. Lin$^1$, Jack C. Lee$^2$ and Shu Y. Yen$^2$

$^1$National Chung Hsing University and $^2$National Chiao Tung University

Abstract: Normal mixture models provide the most popular framework for modelling heterogeneity in a population with continuous outcomes arising in a variety of subclasses. In the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this article, we address the problem of analyzing a mixture of skew normal distributions from the likelihood-based and Bayesian perspectives, respectively. Computational techniques using EM-type algorithms are employed for iteratively computing maximum likelihood estimates. Also, a fully Bayesian approach using the Markov chain Monte Carlo method is developed to carry out posterior analyses. Numerical results are illustrated through two examples.

Key words and phrases: ECM algorithm, ECME algorithm, Fisher information, Markov chain Monte Carlo, maximum likelihood estimation, skew normal mixtures.