A new optimal probability model: Its background and applications to sports and reliability

It has been widely acknowledged that probability-based methodologies play a crucial role in guiding decision-making processes when faced with uncertain or vague circumstances. To ensure that decisions made under such conditions are both meaningful and productive, a variety of methodologies centered around probability have been developed, endorsed, and put into practice. This study also aims to contribute to the existing body of knowledge by introducing a new probability model known as the weighted sine generalized Rayleigh distribution. For the proposed model, certain properties are derived. Furthermore, the parameter estimation technique and simulation studies based on the proposed model are also presented. Finally, the proposed model is successfully implemented on three distinct data sets sourced from sports and different engineering disciplines. By evaluating the statistical significance through the p-value and other various tests, it is evident that the proposed model consistently outperforms its competitor distributions. The practical illustration, emphasizes the efficacy and potential of the proposed model for widespread applications in sports and engineering research and practice.