Multivariate Escher Transformed Laplace Distribution and Its Generalization

Abstract

This paper we introduced a new distribution namely the multivariate Esscher transformed Laplace distribution. Various properties of the distribution are studied and the applications are discussed. Further we develop an autoregressive process with multivariate ETL marginal and study its properties. A Levy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and its marginal distributions are multivariate generalized Esscher transformed Laplace distribution.

Keywords

• Autoregressive processes
• Generalized multivariate Esscher transformed Laplace distribution
• Geometric multivariate Esscher transformed Laplace distribution