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Journal of Probability and Statistics
Volume 2016, Article ID 3509139, 7 pages
http://dx.doi.org/10.1155/2016/3509139
Research Article

A Mixture of Generalized Tukey’s Distributions

Department of Statistics, Universidad Nacional de Colombia, Carrera 45 No. 26-85, Bogotá, Colombia

Received 8 April 2016; Revised 1 July 2016; Accepted 14 July 2016

Academic Editor: Chin-Shang Li

Copyright © 2016 José Alfredo Jiménez and Viswanathan Arunachalam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 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.