Kafi-Pawat Family of Distributions with Applications to COVID-19, Labor Economics, Medical, and Environmental Data

This article presents a novel and flexible family of continuous probability distributions, namely the Kafi-Pawat family of distributions. The Kafi-Pawat family is characterized by two parameters, playing an important role in controlling the shape of the hazard rate function, thereby enhancing its flexibility for modeling diverse data behaviors. We derive key distributional functions of the Kafi-Pawat family, including its hazard rate function. To demonstrate the flexibility and practical utility of the proposed family, we introduce and study several members of the Kafi-Pawat family. The hazard rate functions of all distributions within the Kafi-Pawat family can be monotone or non-monotone, highlighting their flexibility. Parameter estimation is conducted via the method of maximum likelihood. Since the maximum likelihood estimators cannot be obtained in closed form, we employ numerical optimization techniques to obtain the fitted parameter values. The final section is to apply the established distributions to the real-world datasets. Comparative analyses among the considered distributions are performed to exhibit their potential as flexible and effective tool for modeling uncertainty.