The Complementary Asymmetric-Odds Weibull Distribution: A Flexible Lifetime Model with Applications to Hazard Rate Modeling and Change-Point Analysis

This paper introduces the Complementary Asymmetric-Odds Weibull (CAO–W) distribution, a new three-parameter distribution that improves the accuracy of modeling lifetime data with complex behavior. The proposed distribution is based on an asymmetric transformation that combines the baseline distribution with its complement, providing more flexibility when modeling a variety of hazard patterns, such as increasing, decreasing, and bathtub-shaped. Some statistical properties of the CAO–W distribution were studied including a mathematical and graphical analysis of the hazard rate function (HRF). The model parameters were estimated using four widely used estimation approaches: maximum likelihood (ML), least squares (LS), maximum product of spacings (MPS), and the Cramér-von-Mises (CVM). The efficiency of these approaches in estimating the model parameters was investigated through simulation studies under different scenarios. Moreover, the proposed distribution was applied to four real datasets, and compared to some flexible distributions to demonstrate its ability to provide a good fit for lifetime data in survival and reliability analysis applications. Finally, a change point analysis, based on the Minimum Information Criterion (MIC), is also conducted to highlight the flexibility of the proposed model.