A skew–normal mixture of joint location, scale and skewness models

Abstract

Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, 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 paper, we propose and study a novel class of models: a skew–normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew–normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation–Maximization (EM) algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index (BMI) data are presented.