Ghazal M G M, Radwan H M M
Department of Mathematics, Faculty of Science, Minia University, Minia, Egypt.
Department of Mathematics, University of Technology and Applied Sciences-Al Rustaq, 329-Rustaq, Sultanate of Oman.
Math Biosci Eng. 2022 Sep 8;19(12):13193-13213. doi: 10.3934/mbe.2022617.
In this work, we suggest a reduced distribution with two parameters of the modified Weibull distribution to avoid some estimation difficulties. The hazard rate function of the reduced distribution exhibits decreasing, increasing or bathtub shape. The suggested reduced distribution can be applied to many problems of modelling lifetime data. Some statistical properties of the proposed distribution have been discussed. The maximum likelihood is employed to estimate the model parameters. The Fisher information matrix is derived and then applied to construct confidence intervals for parameters. A simulation is conducted to illustrate the performance of maximum likelihood estimation. Four sets of real data are tested to prove the proposed distribution advantages. According to the statistical criteria, the proposed distribution fits the tested data better than some well-known two-and three-parameter distributions.
在这项工作中，我们提出了一种具有两个参数的修正威布尔分布的简化分布，以避免一些估计困难。该简化分布的危险率函数呈现出递减、递增或浴盆形状。所提出的简化分布可应用于许多寿命数据建模问题。已讨论了所提出分布的一些统计特性。采用最大似然法估计模型参数。推导了费希尔信息矩阵，然后将其应用于构建参数的置信区间。进行了模拟以说明最大似然估计的性能。测试了四组实际数据以证明所提出分布的优势。根据统计标准，所提出的分布比一些著名的双参数和三参数分布更适合测试数据。
