A new statistical framework with properties and practical implementation using the time invested in sports training

Abstract

The applications of probability distributions have proven to be impactful across all scientific fields, with notable relevance in sports sciences. In light of this beneficial aspect of probability distributions, this paper puts forth a new probability distribution called the modified trigonometric exponentiated exponential (MTE-exponential) distribution. In this work, we derive various mathematical properties of the MTE-exponential distribution, focusing particularly on those related to quartile characteristics. A widely recognized estimation method is applied to derive the mathematical expressions for the estimators of the MTE-exponential distribution. Furthermore, a simulation analysis is performed to assess the effectiveness of the estimators for different parameter combinations of the MTE-exponential distribution. Finally, an application of the MTE-exponential distribution, which is informed by sports sciences, is presented. The intention behind this presentation is to illustrate the practical applicability of the proposed model. Thus, a comparison is made, utilizing data from sports sciences, between the MTE-exponential distribution and nine other rival distributions including some traditional and modified probability distributions. A thorough examination of four fundamental assessment criteria indicates that the MTE-exponential distribution reliably outperform all conventional and modified probability distributions.