A new multivariate Laplace distribution based on the mixture of normal distributions

Abstract

In this paper, we propose a new multivariate Laplace distribution from normal variance mixture models, called as Type II multivariate Laplace distribution. Unlike the original multivariate Laplace distribution whose all components must have the same value for the mixing variate, the random components in the new distribution could have different value for its own mixing variate and are correlated only through the dependence structure of the normal random vector. Thus, it contains the multiplication of independently identical distribution univariate Laplace distributions as a special case if the normal covariance matrix is diagonal. A tractable stochastic representation is used to derive the probability density function and other statistical properties. The maximum likelihood estimates of parameters via an ECM (expectation/conditional maximization) algorithm and the Bayesian methods are derived. Some simulation studies are conducted to evaluate the performance of the proposed methods. Applications in two real data sets indicate that the Type II multivariate Laplace distribution could have a better performance and is distinct from the original one.