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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.

Keywords

Marshall-Olkin distribution Generalized Pareto distribution Maximum Product Spacing Bayes estimation Monte Carlo simulations.

Article Details

Author Biographies

Hanan Haj AHmad, King Faisal University

Basic Science department , Assistant Professor.

Ehab Almetwally, Institute of Statistical Studies and Research, Cairo University, Cairo, Egypt

Institute of Statistical Studies and Research

How to Cite
Haj AHmad, H., & Almetwally, E. (2020). Marshall-Olkin Generalized Pareto Distribution: Bayesian and Non Bayesian Estimation. Pakistan Journal of Statistics and Operation Research, 16(1), 21-33. https://doi.org/10.18187/pjsor.v16i1.2935