A Discrete Odd Exponentiated Half-Logistic-G Class: Mathematical and Statistical Theory with Goodness-of-Fit Dispersion Data Analysis Across Varied Failure Profiles

Abstract

This article presents a novel discrete class designed to complement the odd exponentiated half-logistic-G class, aiming to offer a versatile probabilistic tool for generalizing diverse discrete baseline models. Upon introduction, the focus shifts to a specific discrete model, where a thorough examination of its mathematical and statistical attributes is conducted. These attributes span the probability mass function, hazard rate function, quantile, crude moments, index of dispersion, entropies, order statistics, and L-moment statistics. The analysis reveals the proficiency of this discrete class in modeling symmetric and asymmetric data across various kurtosis shapes, addressing over dispersion and under dispersion in datasets with outlier observations, and handling different hazard rate patterns, including monotone increasing, monotone decreasing, bathtub, unimodal-bathtub, J-shaped, inverse J-shaped, among others. The estimation of class parameters is discussed using the maximum likelihood approach, and the performance of the estimation method is evaluated using the Markov chain Monte Carlo simulation technique. Finally, the practical utility of the proposed methodology is demonstrated through its application to three real datasets, highlighting its relevance and effectiveness in real-world scenarios.