A New Generalization of Inverse Marshall-Olkin Family and Related Inverse Exponential Model

A new generalization of inverse Marshall-Olkin family

Abstract

In this paper, we introduce a new family of continuous distributions called inverse truncated discrete Mittag-Leffler family of distributions. In particular, we study inverse truncated discrete Mittag-Leffler exponential (GIE) distribution. The GIE distribution contains inverse Marshall-Olkin exponential distribution, inverse generalized exponential distribution and inverse exponential distribution as special case. The density function of GIE distribution is right skewed and has reverse bathtub hazard rate. We derive expression for the moments, generating function, quantiles and R´enyi entropy. Also the stochastic ordering properties are investigated along with the distributions of order statistics. The method of maximum likelihood is used to estimate the model parameters. The existence and uniqueness of maximum likelihood estimates are proved. Simulation studies are also performed. An application to a real data set is presented to illustrate the potentiality of our proposed model.