A new class of skew-symmetric distributions and related families

Abstract

In this work, we investigate a new class of skew-symmetric distributions, which includes the distributions with the probability density function (pdf) given by g _α(x)=2f(x) G(α x), introduced by Azzalini [A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171–178]. We call this new class as the symmetric-skew-symmetric family and it has the pdf proportional to f(x) G _β(α x), where G _β(x) is the cumulative distribution function of g _β(x). We give some basic properties for the symmetric-skew-symmetric family and study the particular case obtained from the normal distribution.

Keywords:

• symmetric-skew-symmetric distribution
• skew-symmetric distribution
• skew-normal distribution
• skew-Cauchy distribution

Acknowledgements

The authors acknowledge helpful comments and suggestions from two referees that substantially improved the presentation. The research of H.W. Gómez and I. Vidal was partially supported by FONDECYT 1090109 grant from Chile. The research of H. Varela was supported by grant DIRINV 1333-07.