A New Family of Continuous Probability Distributions

M El-Morshedy; Fahad Sameer Alshammari; Yasser S Hamed; Mohammed S Eliwa; Haitham M Yousof

doi:10.3390/e23020194

A New Family of Continuous Probability Distributions

Entropy (Basel). 2021 Feb 5;23(2):194. doi: 10.3390/e23020194.

Authors

M El-Morshedy^{1

2}, Fahad Sameer Alshammari¹, Yasser S Hamed³, Mohammed S Eliwa², Haitham M Yousof⁴

Affiliations

¹ Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia.
² Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
³ Department of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi Arabia.
⁴ Department of Statistics, Mathematics and Insurance, Benha University, Benha 13518, Egypt.

Abstract

In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of "Farlie-Gumbel-Morgenstern copula", "the modified Farlie-Gumbel-Morgenstern copula", "the Clayton copula", and "the Renyi's entropy copula" are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to estimate the model parameters. A graphical simulation is performed to assess the finite sample behavior of the estimators of the maximum likelihood method. Two real-life data applications are proposed to illustrate the importance of the new family.

Keywords: Ali-Mikhail-Haq copula; Farlie-Gumbel-Morgenstern; Lomax distribution; clayton copula; compounding; generalized exponential distribution; kernel density estimation; modeling; poisson distribution.