A Mixture of Generalized Tukey’s Distributions

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 family of generalized distributions depend on the parameters, namely, , which controls the skewness. This paper presents the probability density function (pdf) associated with a mixture of Tukey’s family of generalized distributions. The mixture of this class of skewed distributions is a generalization of Tukey’s family of distributions. In this paper, we calculate a closed form expression for the density and distribution of the mixture of two Tukey’s 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.