Marshall-Olkin Generalized Pareto Distribution: Bayesian and Non Bayesian Estimation

Abstract

A new generalization of generalized Pareto Distribution is obtained using the generator Marshall-Olkin distribution (1997). The new distribution MOGP is more flexible and can be used to model non-monotonic failure rate functions. MOGP includes six different sub models: Generalized Pareto, Exponential, Uniform, Pareto type I, Marshall-Olkin Pareto and Marshall-Olkin exponential distribution. We consider different estimation procedures for estimating the model parameters, namely: Maximum likelihood estimator, Maximum product spacing, Least square method, weighted least square method and Bayesian Method. The Bayesian Method is considered under quadratic loss function and Linex loss function. Simulation analysis using MCMC technique is performed to compare between the proposed point estimation methods. The usefulness of MOGP is illustrated by means of real data set, which shows that this generalization is better fit than Pareto, GP and MOP distributions.