A Mixture of Generalized Tukey’s g Distributions

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’s g family 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’s g family of generalized distributions. The mixture of this class of skewed distributions is a generalization of Tukey’s g family of distributions. In this paper, we calculate a closed form expression for the density and distribution of the mixture of two Tukey’s g families 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.