ABSTRACT
We introduce a new model called the length-biased exponential distribution which become a fascinating new model in a number of research domains in recent years. By adding an extra shape parameter, a new generalised form that is coupled to the length-biased exponential distribution addressed in this work may be constructed, enhancing its utility. The new distribution is known as the new extension length-biased exponential distribution (NELBE). Its density function, as well as its survival and hazard rate curves, are all shown graphically. The study presented the quantile function, linear representations, and some other properties. We displayed and graphed the shapes of the distribution functions. When it came time to calculate the distribution parameters, we employed a total of six distinct estimating strategies. In order to compare and draw conclusions about the performance of the different estimators, a thorough numerical analysis was done. Here, two real data set on COVID-19 mortality rate was examined to show how adaptable and practical the suggested distribution is.
ABSTRACT
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 Weibull model without adding any additional parameters. Different distributional properties of the NC-Weibull distribution are obtained. The maximum likelihood approach is implemented to estimate 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 association 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.