A NOVEL MODIFIED EXPONENTIAL-GAMMA DISTRIBUTION:

Abstract

In this paper, a novel univariate continuous lifetime distribution called the Novel Modified New Exponential–Gamma Distribution (NMnEGD) is proposed as a flexible extension of the New Exponential–Gamma family. The proposed distribution is constructed by modifying the New Exponential–Gamma distribution using a generalized gamma–type mechanism, thereby introducing additional shape parameters that enhance modeling flexibility. Several well-known lifetime distributions, including the Exponential, Lindley, Weibull, Gamma, Power Lindley, and Generalized New Exponential–Gamma distributions, are obtained as special cases of the proposed model. The mathematical properties of the NMnEGD are thoroughly investigated, including the probability density function, cumulative distribution function, moments, moment generating function, order statistics, and important reliability characteristics such as the survival function, hazard rate, mean residual life, and mean waiting time functions. Parameter estimation is carried out using the maximum likelihood, least squares, weighted least squares, and Cramér–von Mises estimation methods. The performance of the proposed model is illustrated using a real-life dataset on the strengths of glass fibers. Goodness-of-fit comparisons based on the Akaike Information Criterion, corrected Akaike Information Criterion, Bayesian Information Criterion, and −2 log-likelihood demonstrate the superior fitting ability of the NMnEGD over several existing competing distributions. These results highlight the usefulness of the proposed distribution for modeling lifetime data with diverse hazard rate behaviors.