Constructing a probability distribution of an extended power function with practical application

Abstract

   The process of expanding the probability distributions is one of the important operations that has increased in importance significantly during the past few decades, due to the increase in the ability of classical distributions to represent real data in a broader and more accurate way. In this research, the new exponential family (NEX-Family) was used to build a new probabilistic model called (The New Exponential-X Power function distribution) (NEXPF), and the proposed model is an expansion of the distribution of the power function. As some of its statistical properties were studied, the parameters of the new distribution were estimated in two ways: (the least squares method, the partial estimator’s method). In (Wolfram Mathematica 12.2), several experiments were conducted with small, medium and large sample sizes (100, 75, 50, 25), and the mean square error(MSE)was used to compare the two estimation methods for parameter estimations.