Matrix variate and tensor variate Laplace distributions

Abstract

In this article, we define a matrix variate asymmetric Laplace distribution. We prove some properties of the matrix variate asymmetric Laplace distribution. We prove the relationship between the matrix variate asymmetric Laplace distribution and other distributions. We define a matrix variate generalized asymmetric Laplace distribution. We prove some properties of the matrix variate generalized asymmetric Laplace distribution. We prove the relationship between the matrix variate generalized asymmetric Laplace distribution and other distributions. We define a tensor variate asymmetric Laplace distribution. We prove some properties of the tensor variate asymmetric Laplace distribution. We prove the relationship between the tensor variate asymmetric Laplace distribution and other distributions. We define a tensor variate generalized asymmetric Laplace distribution. We prove some properties of the tensor variate generalized asymmetric Laplace distribution. We prove the relationship between the tensor variate generalized asymmetric Laplace distribution and other distributions.

15 pages