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

Area of Science:

• Statistics
• Probability Theory
• Data Modeling

Background:

• The classical Pareto distribution is widely used for heavy-tailed data.
• Its rigid structure limits its ability to capture diverse tail behaviors and hazard rate patterns.
• Real-world data often exhibit complex tail characteristics not well-represented by the standard Pareto model.

Purpose of the Study:

• To propose a novel extended Pareto (EP) distribution.
• To enhance tail flexibility and accommodate various hazard rate shapes (decreasing, increasing, bathtub).
• To provide a more versatile tool for modeling heavy-tailed phenomena.

Main Methods:

• The extended Pareto distribution is constructed using the modified Fréchet generator applied to the Pareto baseline.
• Key distributional properties (PDF, CDF, quantile function, moments) were derived.
• Parameter estimation employed the method of maximum likelihood, with asymptotic properties established.

Main Results:

• The EP distribution introduces an additional shape parameter, significantly increasing tail flexibility.
• It successfully models a wide range of hazard rate shapes.
• Maximum likelihood estimators demonstrated consistency and efficiency in Monte Carlo simulations.
• The EP model consistently outperformed classical Pareto and other Pareto-type distributions in real-data applications.

Conclusions:

• The proposed extended Pareto distribution offers superior flexibility for modeling heavy-tailed data.
• It provides a powerful and adaptable tool for various scientific and financial applications.
• The EP model represents a significant advancement over the classical Pareto distribution for complex datasets.