Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt.
Comput Intell Neurosci. 2021 Aug 16;2021:9819200. doi: 10.1155/2021/9819200. eCollection 2021.
This paper introduced a relatively new mixture distribution that results from a mixture of Fréchet-Weibull and Pareto distributions. Some properties of the new statistical model were derived, such as moments with their related measures, moment generating function, mean residual life function, and mean deviation. Furthermore , different estimation methods were introduced for determining the unknown parameters of the proposed model. Finally, we introduced three real data sets which were applied to our distribution and compared them with other well-known statistical competitive models to show the superiority of our model for fitting the three real data sets, and we can clearly see that our distribution outperforms its competitors. Also, to verify our results, we carried out the existence and uniqueness test to the log-likelihood to determine whether the roots are global maximum or not.
本文介绍了一种源于 Fréchet-Weibull 和 Pareto 分布混合的新混合分布。推导出了新统计模型的一些性质，如矩及其相关度量、矩生成函数、平均剩余寿命函数和平均偏差。此外，还介绍了确定所提出模型的未知参数的不同估计方法。最后，我们介绍了三个实际数据集，这些数据集应用于我们的分布，并将其与其他著名的统计竞争模型进行了比较，以表明我们的模型在拟合这三个实际数据集方面的优越性，我们可以清楚地看到我们的分布优于其竞争对手。此外，为了验证我们的结果，我们对对数似然进行了存在性和唯一性检验，以确定根是否为全局最大值。
