Rajitha C S, Akhilnath A
Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, India.
Int J Data Sci Anal. 2022 Nov 23:1-21. doi: 10.1007/s41060-022-00369-2.
Creating new distributions with more desired and flexible qualities for modeling lifetime data has resulted in a concentrated effort to modify or generalize existing distributions. In this paper, we propose a new distribution called the power exponentiated Lindley (PEL) distribution by generalizing the Lindley distribution using the power exponentiated family of distributions, that can fit lifetime data. Then the main statistical properties such as survival function, hazard function, reverse hazard function, moments, quantile function, stochastic ordering, MRL, order statistics, etc., of the newly proposed distribution have been derived. The parameters of the distribution are estimated using the MLE method. Then, a Monte Carlo simulation study is used to check the consistency of the parameters of the PEL distribution in terms of MSE, RMSE, and bias. Finally, we implement the PEL distribution as a statistical lifetime model for the COVID-19 case fatality ratio (in %) in China and India, and the new cases of COVID-19 reported in Delhi. Then we check whether the new distribution fits the data sets better than existing well-known distributions. Different statistical measures such as the value of the log-likelihood function, K-S statistic, AIC, BIC, HQIC, and -value are used to assess the accuracy of the model. The suggested model seems to be superior to its base model and other well-known and related models when applied to the COVID-19 data set.
为了对寿命数据进行建模，创建具有更理想和灵活特性的新分布，人们集中精力对现有分布进行修改或推广。在本文中，我们通过使用幂指数族分布对林德利分布进行推广，提出了一种名为幂指数化林德利（PEL）分布的新分布，它可以拟合寿命数据。然后推导了新提出的分布的主要统计特性，如生存函数、危险函数、反向危险函数、矩、分位数函数、随机序、平均剩余寿命、顺序统计量等。使用极大似然估计（MLE）方法估计分布的参数。然后，进行蒙特卡罗模拟研究，以检验PEL分布参数在均方误差（MSE）、均方根误差（RMSE）和偏差方面的一致性。最后，我们将PEL分布作为中国和印度新冠肺炎病死率（以%计）以及德里报告的新冠肺炎新病例的统计寿命模型来实施。然后我们检查新分布是否比现有的知名分布更适合数据集。使用不同的统计量，如对数似然函数值、柯尔莫哥洛夫-斯米尔诺夫（K-S）统计量、赤池信息准则（AIC）、贝叶斯信息准则（BIC）、汉南-奎因信息准则（HQIC）和p值，来评估模型的准确性。当应用于新冠肺炎数据集时，所建议的模型似乎优于其基础模型以及其他知名和相关模型。
