Variance-mean mixture of the multivariate skew normal distribution

Abstract

In this paper, we introduce a new class of multivariate distributions as an extension of the normal variance–mean mixture distributions class. The new class results from a variance-mean mixture of the skew normal and the generalized inverse Gaussian distributions. The new class is very flexible in terms of heavy tails and skewness and many of the widely used distributions, such as generalized hyperbolic, skew t, and skew Laplace distributions are included as special or limiting cases of the new class. An explicit expression for the density function of the new class is given and some of its distributional properties, such as moment generating function, linear transformations, quadratic forms, marginal and conditional distributions are examined. We give a simulation algorithm to generate random variates from the new class and propose an EM algorithm for maximum likelihood estimation of its parameters. We provide some examples to demonstrate the modeling strength of the proposed class.