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 (x)=2f(x) G( x), introduced by Azzalini [A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171178]. We call this new class as the symmetric-skew-symmetric family and it has the pdf proportional to f(x) G ( x), where G (x) is the cumulative distribution function of g (x). We give some basic properties for the symmetric-skew-symmetric family and study the particular case obtained from the normal distribution.