A Mixture of Generalized Tukey’sgDistributions

Abstract

Mixtures of symmetric distributions, in particular normal mixtures as a tool in statistical modeling, have been widely studied. In recent years, mixtures of asymmetric distributions have emerged as a top contender for analyzing statistical data. Tukey’sgfamily of generalized distributions depend on the parameters, namely,g, which controls the skewness. This paper presents the probability density function (pdf) associated with a mixture of Tukey’sgfamily of generalized distributions. The mixture of this class of skewed distributions is a generalization of Tukey’sgfamily of distributions. In this paper, we calculate a closed form expression for the density and distribution of the mixture of two Tukey’sgfamilies of generalized distributions, which allows us to easily compute probabilities, moments, and related measures. This class of distributions contains the mixture of Log-symmetric distributions as a special case.