An Information-Theoretic Approach for Multivariate Skew Laplace Normal Distributions

Abstract

Due to its flexibility, the skew distributions (univariate and multivariate) have received widespread attention over the last two decades because they're become widely used in the modelling and analysis of skewed data sets. The main goal of this paper is to introduce asymptotic expressions for entropy of multivariate skew Laplace normal distribution to deal with the issue by providing a flexible model for modeling skewness and heavy tiredness simultaneously. Thus, we extend this study to the class of mixture model of these distributions. In addition, upper and lower bounds of Rényi entropy of mixture model are found, by using generalized HӦlder’s inequality and some properties of multinomial theorem.. Finally, we give a real data examples to illustrate the behavior of information. A simulation study and a real data example, are also provided to illustrate the information behavior of MSLN and MMSLN distributions for modeling data sets in multivariate settings