El-Morshedy M, Alshammari Fahad Sameer, Hamed Yasser S, Eliwa Mohammed S, Yousof Haitham M
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
Entropy (Basel). 2021 Feb 5;23(2):194. doi: 10.3390/e23020194.
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.
本文推导并研究了一种新的参数化复合G族连续概率分布，称为泊松广义指数G（PGEG）族。推导了相关的数学性质。利用“法利-甘贝尔-摩根斯坦 copula”、“修正的法利-甘贝尔-摩根斯坦 copula”、“克莱顿 copula”和“雷尼熵 copula”定理给出了一些新的二元G族。推导了许多特殊成员，并特别关注指数模型和单参数帕累托II型模型。使用最大似然法估计模型参数。进行了图形模拟以评估最大似然法估计量的有限样本行为。提出了两个实际数据应用案例来说明新族的重要性。
