Integrated modeling of the sports and reliability data: Implications of the probabilistic model and deep learning approaches

In this paper, we consider the evolution of a new probability distribution called the exponential flexible Weibull distribution. The proposed exponential flexible Weibull distribution is obtained by combining the flexible Weibull extension with the exponential T-X strategy. For the exponential flexible Weibull, the estimators of the model parameters are derived mathematically. The appraisal of these parameters is accomplished through a simulation study. The applicability and virtuoso of the exponential flexible Weibull distribution are exemplified via two data sets. Furthermore, we implement the state-of-the-art deep learning algorithms, specifically Artificial Neural Networks and Extreme Gradient Boosting, which are widely employed in real-world applications. A comprehensive comparative analysis is conducted to assess the relative performance of these methodologies.