Nonparametric Bayesian inferences on the skewed data using a Dirichlet process mixture model

This paper presents a new mixture model that can be regarded as a modified version of the Dirichlet process normal mixture models. In this model, the component distribution depends on a parameter whose value affects directly the skewness of the population distribution. Unlike the usual normal mixture model, one can impose prior information on the skewness parameter and make inferences. A nonparametric Bayesian approach is proposed to make inferences about the parameters of the model, including mean, variance, mode, and skewness parameters. An example is given to illustrate the use of the proposed mixture model in testing symmetry and fitting a distribution to data. We also compare our proposed method with two existing methods in terms of mean squared error and mean integrated squared error of the predictive density estimation.