A New Probability Model: Statistical Properties, Estimation, Simulation, and Application

Osama M and Burki I

Published on: 2025-10-15

Abstract

This paper introduces a new probability distribution called the New Modified Exponential Gumbel (NMEG) distribution. The mathematical properties of the proposed distribution are thoroughly investigated, including its quantile function, moments, moment generating function, and order statistics. The maximum likelihood estimation (MLE) method is employed to estimate the parameters of the new model. A simulation study is conducted to assess the performance and consistency of the parameter estimates. The efficiency and applicability of the new model are further demonstrated using a real data set. The results show that the proposed model provides a better fit and demonstrates superiority over several well-known existing models.