Advanced Mathematical Models & Applications

In this research, we present a new four-parameter distribution, called the Kumaraswamy–Pham (Kum Pham) distribution. This model arises from a combination of the Kumaraswamy and Pham distribu tions within the Kumaraswamy generalized family of distributions framework. The Kum-Pham distri bution can represent different hazard rate shapes, including decreasing, increasing, bathtub-shaped, and upside-down bathtub, depending on the parameter settings. Several mathematical properties of the model are studied, such as explicit expressions for the moments, quantile function, mean deviations, entropy measures, and distribution of order statistics. The parameters of the model are estimated through a maximum likelihood approach, and a Monte Carlo simulation is performed for different values of sample sizes to investigate the performance of the estimation technique. The Kum-Pham distribution is shown to provide greater flexibility compared to existing distributions through applica tions to real-world medical datasets.