Nonparametric Mixtures Based on Skew-normal Distributions: An Application to Density Estimation

This article addresses the density estimation problem using nonparametric Bayesian approach. It is considered hierarchical mixture models where the uncertainty about the mixing measure is modeled using the Dirichlet process. The main goal is to build more flexible models for density estimation. Extensions of the normal mixture model via Dirichlet process previously introduced in the literature are twofold. First, Dirichlet mixtures of skew-normal distributions are considered, say, in the first stage of the hierarchical model, the normal distribution is replaced by the skew-normal one. We also assume a skew-normal distribution as the center measure in the Dirichlet mixture of normal distributions. Some important results related to Bayesian inference in the location-scale skew-normal family are introduced. In particular, we obtain the stochastic representations for the full conditional distributions of the location and skewness parameters. The algorithm introduced by MacEachern and Muller in 1998 is used to...