A New Probability Distribution: Model, Theory and Analyzing the Recovery Time Data

Abstract

Probability models are frequently used in numerous healthcare, sports, and policy studies. These probability models use datasets to identify patterns, analyze lifetime scenarios, predict outcomes of interest, etc. Therefore, numerous probability models have been studied, introduced, and implemented. In this paper, we also propose a novel probability model for analyzing data in different sectors, particularly in biomedical and sports sciences. The probability model is called a new modified exponential-Weibull distribution. The heavy-tailed characteristics along with some other mathematical properties are derived. Furthermore, the estimators of the new modified exponential-Weibull are derived. A simulation study of the new modified exponential-Weibull model is also provided. To illustrate the new modified exponential-Weibull model, a practical dataset is analyzed. The dataset consists of seventy-eight observations and represents the recovery time after the injuries in different basketball matches.