Abstract
Statistical methodologies have wider applications in exercise science, sports medicine, sports management, sports marketing, sports science, and other related sciences. These methods can be used to predict the winning probability of a team or individual in a match, the number of minutes that an individual player will spend on the ground, the number of goals to be scored by an individual player, the number of red/yellow cards that will be issued to an individual player or a team, etc. Keeping in view the importance and applicability of the statistical methodologies in sport sciences, healthcare, and other related sectors, this paper introduces a novel family of statistical models called new alpha power family of distributions. It is shown that numerous properties of the suggested method are similar to those of the new Weibull-X and exponential type distributions. Based on the novel method, a special model, namely, a new alpha power Weibull distribution, is studied. The new model is very flexible because the shape of its probability density function can either be right-skewed, decreasing, left-skewed, or increasing. Furthermore, the new distribution is also able to model real phenomena with bathtub-shaped failure rates. Finally, the usefulness/applicability of the proposed distribution is shown by analyzing the time-to-event datasets selected from different football matches during 1964–2018.
Highlights
In the practice of healthcare [1], reliability [2], education [3], hydrology [4], management [5], metrology [6], and sports sciences [7], statistical modeling and predicting real-life events are very crucial
We introduce the proposed family called new alpha power (NAPow) family by using
The NAPow-Weibull model was applied to two datasets taken from the sports sciences
Summary
In the practice of healthcare [1], reliability [2], education [3], hydrology [4], management [5], metrology [6], and sports sciences [7], statistical modeling and predicting real-life events are very crucial. Ahmad et al [19] implemented the T-X approach and introduced an interesting method, namely, a new Weibull-X (NWei-X) family, to update the distributional flexibility of the classical or modified distributions. Ey introduced the NWei-X family by using F[G(y; Φ)] − log(1 − G(y; Φ))/1 − G(y; Φ) in equation (1) with. E traditional exponential, Rayleigh, Weibull, and other extended lifetime distributions belong to the class defined in equation (5) (see [22]). We introduce an additional parameter in equation (5), by replacing the exponent term with α to propose a very flexible family by the DF. Is very interesting and can be useful to generate new statistical models belonging to the T-X family of distributions. Due to an extra parameter in the place of the exponent term in equation (7), the NAPow family delivers greater flexibility
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