On Alpha Power Transformation Generalized Pareto Distribution and Some Properties

Abstract

Recently, the need to develop statistical distributions has become the most important spot. In this context, we employ the α ‐power transformation (APT) method to convert the generalized Pareto distribution (GPD) into a new distribution. Some statistical properties of the proposed distribution are being studied, such as moments, arithmetic mean, moment‐generating function, random variables, entropy, reliability, and hazard function (HF). In addition, the proposed distribution is compared with the Pareto distribution and some other forms of alpha power distributions, such as the alpha power Pareto (APP) distribution, alpha power Rayleigh (APR) distribution, and the alpha power Lomax (APL) distribution. Finally, we demonstrate the benefits of the proposed distribution through a simulation study and two real data sets. It was found that the results showed the MLE method is reliable, the APTGP distribution is a competitive distribution for the aforementioned data set, and it is a mirror image of the Pareto distribution.