An innovative statistical framework with properties and univariate analysis in physical education, reliability engineering, and radiation sector

This study aims to enrich the existing literature on probability-centric methods to more accurately describe and analyze real-world occurrences. Consequently, this research provides a valuable initiative to develop a new class of distributions, named a new beta-power sine-$G$ (NBPS-$G$) distributions. The development of the NBPS-$G$ family is a result of the combination of the versatility of the sine-$G$ method with the novel beta power transformed technique. To demonstrate the NBPS-$G$ in real-world applications, we examine the Weibull distribution as a specific instance, namely, the new beta power sine-Weibull (NBPS-Weibull) distribution. The quantile function of the NBPS-Weibull distribution is computed and then used to determine various other quartile-informed mathematical properties. Additionally, the point estimators are computed, and the findings from the simulation studies are numerically presented. Furthermore, we also explore practical applications of the NBPS-Weibull distribution in a wide range of application areas, such as physical education, reliability engineering, and radiation. The goal is to demonstrate the superiority of the NBPS-Weibull distribution over some existing distributions. Various statistical sources (i.e., certain known statistical tests) indicate that the NBPS-Weibull distribution shows superior effectiveness compared to several alternative methods documented in the literature.