A New Extended Pareto Distribution: Statistical Properties, Estimation, and Applications.

The Pareto distribution is a fundamental model for heavy-tailed data, but its rigid structure often fails to capture the diverse tail behaviors and hazard rate patterns observed in real-world applications. To address this limitation, we propose a new extended Pareto (EP) distribution, obtained by applying the modified Fréchet generator to the classical Pareto baseline. This novel construction introduces an additional shape parameter that enhances tail flexibility and accommodates a wide range of hazard rate shapes, including decreasing, increasing, bathtub, and upside-down bathtub forms. We derive several key distributional properties, including the probability density and cumulative distribution functions, quantile function, and moments. Parameter estimation is carried out using the method of maximum likelihood, and the asymptotic properties of the estimators are established. Monte Carlo simulations confirm the consistency and efficiency of the estimators. The practical utility of the EP model is demonstrated through applications to diverse real datasets, where it consistently outperforms classical Pareto and other Pareto-type competitors based on likelihood-based criteria and goodness-of-fit tests. The proposed distribution provides a powerful new tool for modeling heavy-tailed phenomena in economics, finance, reliability, hydrology, and environmental sciences.