A new tangent Weibull distribution with applications in sports and radiation sciences

Empirical studies have shown that recent research has focused on developing and updating existing data analysis methods to provide the best possible description of the phenomena under study. These methods are yielding significant advantages and meeting today’s demand for best-fitting real-world events. Therefore, we focus on this important research area and develop a new data analysis method designed to provide optimal descriptions of complex events in application domains. The proposed method is centered on the implication of the tangent function and is thus termed a novel tangent-G method. Based on the novel tangent-G method, we propose a new probability distribution, refereed to as a new tangent-Weibull (NT-Weibull) distribution For the NT-Weibull distribution, we establish several mathematical properties and calculate the maximum likelihood estimator. Furthermore, we also consider simulation-based analytical study. Following theoretical, mathematical calculations, and simulation studies, we also consider the application of the NT-Weibull distribution in real-world scenarios. We validate this fact using sports and radiation-related data sets. Based on these two data sets, we compare the NT-Weibull distribution with other distributions. Both numerical results and visualization methods confirm the superiority of the NT-Weibull distribution in particular case scenarios.