Notes on a modified exponential-Gamma distribution: Its properties and applications

Abstract

Accurate Modeling and analysis of real-world data playa vital role across various fields, enabling better decision-making and predictions. While it is widely acknowledged that “all models are wrong, but some are useful.” Nevertheless, researchers continuously develop, modify, extend, generalize and combine models with other distributionsto enhance accuracy and achieve significant progress. This paper introduces the Exponentiated Generalized new Exponential-Gamma distribution (EGnEG), a novel four parameters univariate continuous lifetime probability distribution that extends the new Exponential-Gamma distribution. The proposed distribution is named the Exponentiated Generalized new Exponential-Gamma distribution (EGnEG). Its survival and hazard rate functions of the distribution were derived and analyzed visually to understand its properties. Graphical representations of the probability density function (PDF), cumulative distribution function (CDF) and hazard rate function illustrate the distribution’s behaviors across different parameter values.Additionally, Entropy measures and order statistic were determined to further assess its characteristics. The parameters of the EGnEG distribution were estimated using three different methods: Maximum Likelihood Method (MLE), Least Squares Estimation (LSE), and Cramer-Von-Mises Estimation (CVME). To assess its Goodness-of-fit, the distribution was applied to a real-life dataset and compared with that of some existing related distributions. The comparison based on the values of , Akaike Information Criteria (AIC) Bayesian Information Criteria (BIC).The results from the dataset indicate that the Exponentiated Generalized New Exponential-Gamma (EGnEG) distribution out performs other competing distributions considered in the study. Therefore, this new distribution is recommended as a valuable alternative for modeling real life datasets, offering improved flexibility and accuracy in statistical modeling.