A new Cosine-Weibull model: Distributional properties with applications to basketball and medical sectors

The two-parameter classical Weibull distribution is commonly implemented to cater for the product's reliability, model the failure rates, analyze lifetime phenomena, etc. In this work, we study a novel version of the Weibull model for analyzing real-life events in the sports and medical sectors. The newly derived version of the Weibull model, namely, a new cosine-Weibull (NC -Weibull) distribution. The importance of this research is that it suggests a novel version of the Wei-bull model without adding any additional parameters. Different distributional properties of the NC-Weibull distribution are obtained. The maximum likelihood approach is implemented to esti-mate the parameters of the NC-Weibull distribution. Finally, three applications are analyzed to prove the superiority of the NC-Weibull distribution over some other existing probability models considered in this study. The first and second applications, respectively, show the mortality rates of COVID-19 patients in Italy and Canada. Whereas, the third data set represents the injury rates of the basketball players collected during the 2008-2009 and 2018-2019 national basketball associ-ation seasons. Based on four selection criteria, it is observed that the NC-Weibull distribution may be a more suitable model for considering the sports and healthcare data sets.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).

Bayesian Inferential Approaches and Bootstrap for the Reliability and Hazard Rate Functions under Progressive First-Failure Censoring for Coronavirus Data from Asymmetric Model

This paper deals with the estimation of the parameters for asymmetric distribution and some lifetime indices such as reliability and hazard rate functions based on progressive first-failure censoring. Maximum likelihood, bootstrap and Bayesian approaches of the distribution parameters and reliability characteristics are investigated. Furthermore, the approximate confidence intervals and highest posterior density credible intervals of the parameters are constructed based on the asymptotic distribution of the maximum likelihood estimators and Markov chain Monte Carlo technique, respectively. In addition, the delta method is implemented to obtain the variances of the reliability and hazard functions. Moreover, we apply two methods of bootstrap to construct the confidence intervals. The Bayes inference based on the squared error and LINEX loss functions is obtained. Extensive simulation studies are conducted to evaluate the behavior of the proposed methods. Finally, a real data set of the COVID-19 mortality rate is analyzed to illustrate the estimation methods developed here. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.