Applied Statistics & Insurance Department, Faculty of Commerce Mansoura University, Mansoura, Egypt.
Department of Statistics, Faculty of Business Administration, Delta University of Science and Technology, Gamasa, Egypt.
PLoS One. 2022 Oct 21;17(10):e0276181. doi: 10.1371/journal.pone.0276181. eCollection 2022.
Since the spread of COVID-19 pandemic in early 2020, modeling the related factors became mandatory, requiring new families of statistical distributions to be formulated. In the present paper we are interested in modeling the vaccination rate in some African countries. The recorded data in these countries show less vaccination rate, which will affect the spread of new active cases and will increase the mortality rate. A new extension of the inverted Nadarajah-Haghighi distribution is considered, which has four parameters and is obtained by combining the inverted Nadarajah-Haghighi distribution and the odd Lomax-G family. The proposed distribution is called the odd Lomax inverted Nadarajah-Haghighi (OLINH) distribution. This distribution owns many virtuous characteristics and attractive statistical properties, such as, the simple linear representation of density function, the flexibility of the hazard rate curve and the odd ratio of failure, in addition to other properties related to quantile, the rth-moment, moment generating function, Rényi entropy, and the function of ordered statistics. In this paper we address the problem of parameter estimation from frequentest and Bayesian approach, accordingly a comparison between the performance of the two estimation methods is implemented using simulation analysis and some numerical techniques. Finally different goodness of fit measures are used for modeling the COVID-19 vaccination rate, which proves the suitability of the OLINH distribution over other competitive distributions.
自 2020 年初 COVID-19 大流行以来，对相关因素进行建模已成为强制性要求，需要制定新的统计分布族。在本文中，我们有兴趣对一些非洲国家的疫苗接种率进行建模。这些国家的记录数据显示疫苗接种率较低，这将影响新的活跃病例的传播，并会增加死亡率。考虑了倒置的纳拉亚哈-哈格希吉分布的一个新扩展，它有四个参数，通过组合倒置的纳拉亚哈-哈格希吉分布和奇数 Lomax-G 族获得。建议的分布称为奇数 Lomax 倒置纳拉亚哈-哈格希吉（OLINH）分布。该分布具有许多优良特性和吸引人的统计特性，例如密度函数的简单线性表示、风险率曲线的灵活性和故障的奇数比，此外还有与分位数、第 r 个矩、矩生成函数、Renyi 熵和有序统计函数相关的其他特性。在本文中，我们从最频繁和贝叶斯方法的角度解决参数估计问题，因此通过模拟分析和一些数值技术来实现两种估计方法的性能比较。最后，使用不同的拟合优度度量来对 COVID-19 疫苗接种率进行建模，这证明了 OLINH 分布优于其他竞争分布的适用性。
