The Marshall-Olkin length-biased exponential distribution and its applications

Abstract

A generalization of the length-biased exponential distribution called the Marshall-Olkin length-biased exponential distribution is proposed in the present paper. Statistical properties of the proposed model are discussed. The parameters of the proposed model are estimated by maximum likelihood estimation method. The performance of the maximum likelihood estimates is investigated by means of a Monte Carlo simulation study. The appropriateness of the model is validated empirically by utilizing a real life data set. Keywords: Length-biased exponential, Marshall-Olkin, Order statistic, Rényi entropy