On the empirical exploration of a new probability distribution in physical education and reliability

Abstract

Probability-based methodologies have gained widespread recognition for their pivotal role in steering decision-making in contexts marked by uncertainty or vagueness. In order to guarantee that decisions made in these circumstances are both significant and impactful, various methodologies focused on probability have been devised and utilized. This study seeks to significantly enrich the existing literature by proposing a new probability model termed the weighted sine exponentiated Weibull distribution. Certain characteristics are obtained for the suggested model. Additionally, the parameter estimation method and simulation studies related to the suggested model are also provided. Two distinct data sets, acquired from the disciplines of physical education and reliability, were effectively implemented using the proposed model, resulting in a successful outcome. Through the utilization of the $p$-value and various tests, it becomes apparent that the weighted sine exponentiated Weibull model consistently surpasses its competitor distributions in terms of statistical significance. The proposed model’s practical illustration highlights its effectiveness and potential for extensive use in both physical education and reliability research and practice.