A New Flexible Marshall–Olkin Extended Odd Weibull–G Family of Distributions: Theory, Properties and Applications

Abstract

In this paper, we introduce the Marshall–Olkin Extended Odd Weibull–G (MO–ExOW–G) family of distributions (FoD), as a flexible framework for modeling lifetime data characterized by skewness, heavy tails, and complex hazard rate structures. The proposed family integrates the Marshall–Olkin (MO) generator with the Extended Odd Weibull–G (ExOW–G) family to enhance shape adaptability and tail behavior. This combination enables the new MO-ExOW-G to capture a wide spectrum of hazard rate forms, including increasing, decreasing, unimodal, bimodal, bathtub, and inverse bathtub patterns. We derive some statistical properties of the MO–ExOW–G family. Parameter estimation is addressed through various techniques, and the performance of the estimators is assessed via Monte Carlo simulations. Special cases of the MO-ExOW-G are applied to real-world datasets from clinical studies and engineering contexts, where the proposed models exhibit superior goodness-of-fit compared to several established alternatives. Overall, the MO–ExOW–G FoD provides a powerful and unified approach for analyzing survival and reliability data, offering substantial improvements in flexibility and interpretability.