A discrete odd exponentiated half-logistic-G class: Mathematical and statistical theory with Goodness-of-fit dispersion data analysis across varied failure profiles

The paper introduces a novel discrete probability class specifically designed to extend the odd exponentiated half-logistic-G family, providing a flexible framework for generalizing various discrete baseline models. The study begins with the formulation of the new discrete class, followed by an in-depth analysis of a particular discrete model within this framework. A comprehensive investigation of its mathematical and statistical properties is conducted, covering key characteristics such as the probability mass function, hazard rate function, crude moments, index of dispersion, entropy measures, order statistics, and L-moments. The findings demonstrate the model’s ability to effectively capture both symmetric and asymmetric data distributions while accommodating a broad range of kurtosis structures. Additionally, the proposed class proves adept at addressing overdispersion and underdispersion in datasets with outliers, as well as modeling diverse hazard rate patterns, including monotonically increasing and decreasing trends, bathtub-shaped, unimodal-bathtub, J-shaped, inverse J-shaped, and other complex forms. Parameter estimation for the proposed class is carried out using the maximum likelihood method, with the accuracy and efficiency of the estimation process assessed through Markov chain Monte Carlo simulations. To validate its practical applicability, the new probability generator is applied to three real-world datasets, demonstrating its robustness and effectiveness in capturing real data patterns.