A Generalization of the Marshall-Olkin Bivariate Pareto Distribution and its Parameter Estimation

Yuxiang Yang

doi:10.6919/ICJE.202601_12(1).0012

Authors

Yuxiang Yang

DOI:

https://doi.org/10.6919/ICJE.202601_12(1).0012

Keywords:

Marshall-Olkin Bivariate Pareto Distribution; Proportional Reversed Hazard Rate Parameter; Maximum Likelihood Estimators; EM Algorithm.

Abstract

As a generalization of the Marshall-Olkin bivariate Pareto distribution proposed by Kumar Dey and Paul, we introduce the proportional reversed hazard rate Marshall-Olkin bivariate Pareto distribution (PRH-MOBVPA) and the Block-Basu proportional reversed hazard rate bivariate Pareto distribution (PRH-BBBVPA). This paper investigates the relevant probabilistic properties of these two distributions, including expressions for their joint probability density function, joint survival function, probability density functions of marginal distributions and conditional distributions. Additionally, by comparing surface plots and contour plots of the joint density function of the PRH-BBBVPA distribution under different parameters, we reveal how its joint density function varies with different parameters. Furthermore, the maximum likelihood estimators of the six parameters of the PRH-MOBVPA distribution are derived via the expectation-maximization (EM) algorithm.

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