A modified cosine-based probability distribution: Its mathematical features with statistical modeling in sports and reliability prospects

Statistical analysis of real-world data sets is an invaluable tool for guiding researchers in making informed decisions in various applied fields, especially when faced with uncertainty. Over time, a wide array of probability distributions have been developed and applied in diverse ways across different sectors. A substantial body of literature exists on these distributions, with new parameters continuously being added, increased up to eight. This particular research work also gives rise to a novel probabilistic model known as the weighted sine very flexible-Weibull distribution. Comprising the very flexible Weibull model and a sine-oriented approach, the weighted sine very flexible-Weibull distribution is characterized by quartile-based properties. In addition to these properties, estimators for the new model are also established. The estimation aspect of the weighted sine very flexible-Weibull distribution is further enhanced through a simulation study. Finally, the application of the weighted sine very flexible-Weibull distribution is demonstrated using three practical data sets taken from the sports and reliability sciences. After considering various evaluation criteria, it has been determined that the weighted sine very flexible-Weibull distribution offers the best fit for the sports and reliability data sets.