A New KM-H Family: Estimation, Applications and Regression Modeling

Given the increasing complexity of real-world phenomena, the development of new probability distributions and families has become increasingly important. Building on the Kavya–Manoharan (KM) transformation, we propose a new family of distributions named the new KM-H family. This family is constructed by introducing an innovative transformation into the KM framework, improving modeling flexibility while maintaining parameter parsimony. The novel KM-Weibull distribution (NKM-W) is investigated as a special case of the proposed family, and several statistical features are derived. Analytical and graphical findings indicate that the model is effective in modeling complex data and reliability applications. The NKM-W parameters are estimated using maximum likelihood, percentile, ordinary least squares, weighted least squares, and Cramér–von Mises methods. The performance of these methods is assessed using Monte Carlo simulation study. Three real-world engineering datasets are investigated to demonstrate the applicability of the NKM-W, which provides a highly competitive fit relative to several classical and generalized lifetime distributions. Additionally, a regression model is developed through log-location-scale reparametrization of the NKM-W distribution and evaluated using two medical datasets. The findings demonstrate the competitive efficacy of the introduced log NKM-W regression model compared to the investigated regression models.