Abstract

In this article, we introduce a new family of distributions namely, Marshall-Olkin generalized Esscher transformed Laplace distribution, which is a generalization of the three parameter Esscher transformed Laplace distribution. We obtain explicit forms for their density, distribution function and Hazard function. Properties of the distribution are studied and a real application of the distribution is considered. We also derive an AR (1) process with Marshall-Olkin generalized Esscher transformed Laplace distribution as stationary marginal and its properties are studied. The Kumaraswamy generalization of the Marshall-Olkin generalized Esscher transformed Laplace distribution is proposed along with its properties.

Author: Rimsha H and Dais George

Received on: July, 2021

Accepted on: March, 2022