A New Family of Continuous Probability Distributions |
| |
| Authors: | M El-Morshedy Fahad Sameer Alshammari Yasser S Hamed Mohammed S Eliwa Haitham M Yousof |
| |
| Institution: | 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: | poisson distribution generalized exponential distribution compounding Farlie-Gumbel-Morgenstern clayton copula Ali-Mikhail-Haq copula modeling Lomax distribution kernel density estimation |
|
|
