Tangent exponential-G family of distributions with applications in medical and engineering

This study introduces a novel family of probability distributions called the ”tangent exponential-G family,” which is derived using trigonometric transformations of the exponential distribution. The significance of this research lies in developing new statistical models with versatile hazard functions, including j-shaped, S-shaped, increasing, and bathtub shapes. The primary aim is to construct and analyze the properties of this new distribution family. We utilized the exponential distribution function and applied the tangent transformation to develop the tangent exponential-G family. Key statistical properties and characteristics of this family are explored. Parameter estimation is performed using different estimation methods, and its accuracy is confirmed through simulation studies, which show reduced biases and mean square errors with increasing sample sizes. We tested the proposed distribution with real-world data sets to demonstrate practical applicability. Comparative analyses using model selection criteria and goodness-of-fit tests reveal that the tangent exponential-G family and its sub-model outperform compared to existing models, indicating its robustness and utility in statistical modeling.