Abstract: This article studies a family of multivariate skew-symmetric distributions. We show that any multivariate probability density function admits a skew-symmetric representation. We derive several characteristics of this representation and establish an invariance property. We present a stochastic representation of skew-symmetric distributions which lends itself readily to simulations. The flexibility of skew-symmetric distributions is illustrated through several graphical examples.
Key words and phrases: Elliptical, kurtosis, multimodality, quadratic form, skewness, Stochastic representation.