A state-of-the-art statistical tool with Monte Carlo simulation and practical applications in sports and radiation sciences

One of the focuses of the statistical research is to develop new classifications of probability models for data analysis across different application areas. To further strengthen this research area, this paper also proposes a new method that incorporates the characteristics of a trigonometric function, especially the sine function. The novel distribution approach we introduce is called the new sine trigonometric-$G$ (NST-$G$) family of distributions. Using the NST-$G$ technique, we study a new variant of the Weibull model, specifically a new sine trigonometric-Weibull (NST-Weibull) distribution. We demonstrate visually that the NST-Weibull distribution, due to the inclusion of the sine function, provides enhanced flexibility in its density and hazard functions. Some properties of the NST-Weibull distribution, especially those related to quartiles, are mathematically derived. The estimators of the NST-Weibull distribution are derived using the maximum likelihood method. Furthermore, the Monte Carlo simulation analysis is performed to evaluate the validity of the estimators. Finally, the NST-Weibull distribution is demonstrated through two application cases in sports and radiation science. Using four statistical criteria, we find that the NST-Weibull distribution has significantly better and more optimal fitting ability compared to existing models.