A new flexible Weibull distribution for modeling real-life data: Improved estimators, properties, and applications

In this paper, we proposed a novel and flexible lifetime model, the generalized Kavya–Manoharan Weibull distribution, which can be interpreted as a proportional reversed hazard model. The most remarkable feature of the proposed model is its ability to effectively capture a wide range of hazard rate patterns using only three parameters. These include decreasing, J-shaped, reverse J-shaped, and increasing patterns, as well as key nonmonotonic shapes such as the bathtub, modified bathtub, and upside-down bathtub shapes. Additionally, its density can exhibit right-skewness, left-skewness, symmetry, and reversed-J shapes. We explored several distributional properties of the proposed model and estimated its parameters using eight methods. The effectiveness of these estimators was validated through extensive simulation studies. Furthermore, we assessed the versatility of the proposed distribution using three real-world datasets, demonstrating its exceptional capacity to fit the data accurately. Our results indicated that the proposed distribution outperforms several existing generalizations of the Weibull distribution in terms of fit quality.