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

A significant aspect of probability distributions lies in their relevance to practical applications. Nevertheless, not all probability distributions yield adequate results across various scenarios. Consequently, there is a continuous need to explore the creation of new probability distributions. This paper delves into this intriguing research domain by presenting a novel probability distribution that incorporates two established trigonometric functions. The suggested model represents an innovative sine–cosine extension of the Weibull distribution, referred to as the modified sine–cosine Weibull (MSC-Weibull) distribution. A notable characteristic of the MSC-Weibull distribution is its lack of additional parameters, thereby circumventing the complications associated with re-parameterizations. The estimators for the MSC-Weibull distribution are derived through mathematical methods. A concise statistical study (simulation study) is conducted to evaluate the reliability of these estimators. Additionally, specific mathematical properties related to the MSC-Weibull distribution are established using its quartile function. The relevance of the MSC-Weibull distribution is confirmed by analyzing two practical data sets. The first data set originates from the domain of sports sciences, while the second is linked to reliability studies. Through the application of four established optimality criteria, it is apparent that the MSC-Weibull distribution significantly enhances the process of data analysis.