Abstract

Statistical modeling of the practical data sets is a useful method that guides researchers to make decisions under uncertainty in applied sectors. To date, a rich number of probability distributions have appeared that have been developed in different ways and implemented in different fields. A vast literature of the available distributions have been constructed by adding new additional parameters, varying from one to eight. This specific piece of the research work also prompts a new probabilistic model, namely, the weighted sine flexible-Weibull distribution. The weighted sine flexible-Weibull distribution consists of the flexible Weibull extension model and a sine-oriented methodology. For the weighted sine flexible-Weibull distribution, the quartile-based properties are derived. Besides these properties, the estimators for the new model are also derived. The estimation part of the weighted sine flexible-Weibull distribution is further extended by conducting a simulation study. Finally, the weighted sine flexible-Weibull distribution is illustrated by considering the injury rate in logistics and public transport systems that are reported after the safety factors are considered. Based on several evaluation criteria, it is established that the weighted sine flexible-Weibull distribution provides the optimal fitting to the injury rate data.