In this article, we introduce the multivariate slash and skew-slash t distributions which provide alternative choices in simulating and fitting skewed and heavy tailed data. We study their relationships with other distributions and give the densities, stochastic representations, moments, marginal distributions, distributions of linear combinations and characteristic functions of the random vect...

Non-normal mixture distributions have received increasing attention in recent years. Finite mixtures of multivariate skew-symmetric distributions, in particular, the skew normal and skew t-mixture models, are emerging as promising extensions to the traditional normal and t-mixture models. Most of these parametric families of skew distributions are closely related, and can be classified into fou...

By using well known properties of elliptical distributions we show that the relation between Kendall's tau and the linear correlation coefficient for bivariate normal distributions holds more generally (subject to only slight modifications) for the class of elliptical distributions.

We develop a Bayesian approach for the selection of skew in multivariate skew t distributions constructed through hidden conditioning in the manners suggested by either Azzalini and Capitanio (2003) or Sahu, Dey and Branco (2003). We show that the skew coefficients for each margin are the same for the standardized versions of both distributions. We introduce binary indicators to denote whether ...

The stochastic data envelopment analysis (SDEA) was developed considering the value ofinputs and outputs as random variables. Therefore, statistical distributions play an importantrole in this regard. The skew-normal (SN) distribution is a family of probability densityfunctions that is frequently used in practical situations. In this paper, we assume that the inputand output variables are skew-...

Most financial models for modelling dependent risks are based on the assumption of multivariate normality and linear correlation is used as a measure of dependence. However, observed financial data are rarely normally distributed and tend to have marginal distributions with heavier tails. Furthermore, the observed synchronized extreme falls in financial markets can not be modelled by multivaria...

In this paper, a class of multivariate skew distributions has been explored. Then its properties are derived. The relationship between the multivariate skew normal and the Wishart distribution is also studied. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords-Skew normal distribution, Wishart distribution, Moment generating function, Moments. Skewness.

Several matrix variate hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted hypergeometric type distributions with matrix arguments are then proposed. The scale mixture of left-spherical matrix variate elliptical distributions and univariate inverted hypergeometric type distributions is also derived as a...