A new generalization of the Pareto distribution and its applications

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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability

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ISSN: 1234-7655
eISSN: 2450-0291

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VOLUME 21 , ISSUE 5 (December 2020) > List of articles

A new generalization of the Pareto distribution and its applications

Ehab M. Almetwally / Hanan A. Haj Ahmad

Keywords : Marshall-Olkin distribution, alpha power transformation, maximum likelihood estimator, maximum product spacings, Bayes estimation, simulation

Citation Information : Statistics in Transition New Series. Volume 21, Issue 5, Pages 61-84, DOI: https://doi.org/10.21307/stattrans-2020-055

License : (CC BY-NC-ND 4.0)

Received Date : 26-March-2020 / Accepted: 11-May-2020 / Published Online: 20-December-2020

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ABSTRACT

This paper introduces a new generalization of the Pareto distribution using the MarshallOlkin generator and the method of alpha power transformation. This new model has several desirable properties appropriate for modelling right skewed data. The Authors demonstrate how the hazard rate function and moments are obtained. Moreover, an estimation for the new model parameters is provided, through the application of the maximum likelihood and maximum product spacings methods, as well as the Bayesian estimation. Approximate confidence intervals are obtained by means of an asymptotic property of the maximum likelihood and maximum product spacings methods, while the Bayes credible intervals are found by using the Monte Carlo Markov Chain method under different loss functions. A simulation analysis is conducted to compare the estimation methods. Finally, the application of the proposed new distribution to three real-data examples is presented and its goodness-of-fit is demonstrated. In addition, comparisons to other models are made in order to prove the efficiency of the distribution in question.

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