Structural Properties of the Alpha Power Exponentiated Generalized Pareto Distribution with Applications

In this article, we introduce a new distribution developed using the alpha power transformation, called the alpha power exponentiated generalized Pareto distribution. This distribution is particularly useful for analyzing heavy-tailed data and for financial risk management. We provide important mathematical properties of the proposed distribution, including its linear representation, moment-generating function, moments, and order statistics. The model parameters are estimated using the methods of maximum likelihood, least squares, and Cramér–von Mises estimation. We evaluate the performance of these estimation methods through simulation studies. Additionally, we apply the APEGP distribution to real-life financial data and demonstrate its effectiveness in calculating Value at Risk, showcasing its suitability for assessing potential losses in financial contexts.