Elgarhy Mohammed, Kayid Mohamed, Elbatal Ibrahim, Muhammad Mustapha
Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt.
Department of Basic Sciences, Higher Institute of Administrative Sciences, Belbeis, AlSharkia, Egypt.
Heliyon. 2024 Aug 20;10(16):e36348. doi: 10.1016/j.heliyon.2024.e36348. eCollection 2024 Aug 30.
In this study, we introduce a new extension of the Fréchet distribution known as the new extended Fréchet (NE_Fr) model. The NE_Fr is created by combining the new extended family of distributions and the Fréchet distribution. The NE_Fr has more flexibility than the classical Fréchet distribution and some generalizations of the Fréchet distribution. The probability density function of the NE_Fr can be decreasing, unimodal and right skewed shape but it's hazard rate function can be decreasing or up-side-down shape. Several mathematical properties of the new model were derived by calculating the quantile function, the ordinary moments, the incomplete moments, the moment generating function, the conditional moment, the Bonferroni curve and the Lorenz curve. Several entropy measures were developed for this purpose. The inferences from the NE_Fr distribution were investigated using several established methods such as maximum likelihood estimation, least squares and weighted least squares estimation, and Anderson-Darling estimation. The simulation results demonstrated the computational efficiency of these techniques. The proposed NE_Fr distribution was demonstrated to be useful by examining three actual data sets.
在本研究中，我们引入了一种新的弗雷歇分布扩展，即新扩展弗雷歇（NE_Fr）模型。NE_Fr是通过将新扩展的分布族与弗雷歇分布相结合而创建的。NE_Fr比经典弗雷歇分布以及弗雷歇分布的一些推广具有更大的灵活性。NE_Fr的概率密度函数可以是递减的、单峰的且右偏的形状，但其风险率函数可以是递减的或倒U形的。通过计算分位数函数、普通矩、不完全矩、矩生成函数、条件矩、邦费罗尼曲线和洛伦兹曲线，推导了新模型的几个数学性质。为此开发了几种熵度量。使用几种既定方法，如最大似然估计、最小二乘法和加权最小二乘法估计以及安德森 - 达林估计，研究了来自NE_Fr分布的推断。模拟结果证明了这些技术的计算效率。通过检验三个实际数据集，证明了所提出的NE_Fr分布是有用的。
