A new tangent-based probabilistic approach with applications in sports and medical sciences

This paper proposes a new probabilistic method using the tangent function, namely, a new tangent-F family of distributions. It improves the data-fitting ability of its special members by adding a parameter. Some properties of the new tangent-F approach are derived. Based on the new tangent-F method, we study a new interesting probability model called a new tangent flexible-Weibull distribution. We implement the maximum likelihood method to derive the new tangent flexible-Weibull distribution estimators. A simulation study is performed for evaluating the new tangent flexible-Weibull distribution estimators. These estimators are evaluated using two statistical criteria. Finally, we illustrate the new tangent flexible-Weibull distribution by considering two applications (i.e., two data examples). The first data example is considered from sports science. It represents the waiting time until the first goal is scored in different 78 football matches. Another data example is considered from medical science. This represents the survival times of 32 patients affected by acute myelogenous leukemia. Using seven decision criteria, it is shown that the new tangent flexible-Weibull distribution outperforms rival distributions. The results lead to the fact that the new tangent-F method significantly improves the data fitting ability of its special members.