A new cosine-based approach for modelling the time-to-event phenomena in sports and engineering sectors

Data analysis through probability-based methods plays an important role in decision-making in all spheres of life. Probability-based approaches lead to productive decision-making under uncertainty. To date, several probability distributions have been formulated that are characterized in different ways and successfully applied in various fields. Most of these probability distributions are studied by adding many additional parameters, typically from one to eight. There is the very least number of available distributional methodologies that are devised without inducing new parameters. In this integrated research piece of work, we provide a new cosine-adaptive method that is developed without considering any new parameters. We call the proposed method the weighted cosine-K family of distributions. Focusing on the proposed method, a new probability model is developed that is named the weighted cosine-Weibull (WC-Weibull) distribution. Some quartile-based characteristics along with estimators of the WC-Weibull distribution are derived. For the parameters of the WC-Weibull distribution, the point estimators are derived. The assessment of point estimators of the WC-Weibull distribution's parameters is provided through a simulation study. Finally, the utility of the WC-Weibull distribution is demonstrated by considering time-to-event phenomena in sports and the engineering sectors. Considering four statistical criteria, it has been shown that the WC-Weibull distribution is an efficient and optimal model for time-related facts (or events) in sports and engineering fields.