Development of a novel odd Weibull-half logistic distribution: Mathematical properties and applications

Abstract

Classical lifetime models such as the Half Logistic (HL) and Weibull distributions, though widely applied in reliability and survival analysis, often exhibit limitations in capturing complex data structures such as heavy tails, multimodality, or non-monotonic hazard rate patterns. To overcome these shortcomings, this study proposes a novel and more flexible model called the Odd Weibull – Half Logistic (OW-HL) distribution. By integrating the Weibull generator with the Half Logistic baseline, the OW–HL distribution extends the modeling capability of its predecessors, providing a wide range of shapes for its probability density and hazard functions, including increasing, decreasing, bathtub, and unimodal forms. Several theoretical properties of the proposed model are derived, including moments, quantile function, entropy measures, and order statistics. Parameter estimation was performed using the maximum likelihood approach, and the efficiency of the estimators was evaluated via a comprehensive Monte Carlo simulation assessing bias, mean square error, confidence interval length, and coverage probability. Applications to three real datasets spanning materials strength and energy consumption data revealed that the OW–HL distribution consistently provides superior goodness-of-fit compared to existing competitors such as Weibull, Exponentiated Weibull, Log-Logistic, and Lomax distributions. The results confirmed the model’s robustness, flexibility, and practical utility for modeling asymmetric and heavy-tailed data in applied sciences.