A new updated version of the Weibull model with an application to re-injury rate data

Abstract

Probability distributions play useful and meaningful roles in sports sciences and biomedical sectors. Probability distributions can be used to model and predict the chances of injuries and recovery time after the injuries. We propose and implement a new method to introduce new probability distributions. The new method is named a new updated-V family, as it can be used to increase/update the flexibility of the modified and traditional probability models. Based on the new updated-V method, a new extension of the Weibull model, namely, a new updated Weibull model is proposed. Statistical properties of the new updated-Weibull model, such as (i) quantile function, (ii) heavy-tailed properties (iii) rth moment, (iv) probability weighted moments, and (i) moment generating functions are presented. For the new updated-V distributions, the estimators are derived. The assessment of the new updated-V distribution estimators is done via a simulation study. A practical application related to the re-injury rate data is considered for the establishment of the applicability of the new updated Weibull distribution.

Keywords

• Weibull distribution
• Biomedical science
• Football injuries
• Mathematical properties
• Statistical modeling