The Mgamma Distribution: Statistical Properties and Application to Real-life Data

Abstract

We propose a new one-parameter continuous distribution, termed the Mgamma distribution, obtained as a finite mixture of two Gamma components having different shapes. Key statistical properties are derived, including moments, generating functions, stochastic ordering, and reliability measures such as hazard rate and mean residual life. Parameter estimation is addressed
using the method of moments and maximum likelihood, with simulation studies confirming the consistency and efficiency of estimators. The applicability of the Mgamma distribution is demonstrated on four real datasets from engineering, hydrology, medicine, and queueing systems. Model selection criteria (AIC, BIC, CAIC) and goodness-of-fit tests (KS, Cram ́er–von Mises, Anderson–Darling) consistently show that Mgamma provides a superior fit compared to classical models such as Exponential, Lindley, Xgamma, Shanker, and Akash distributions. These findings establish Mgamma as a flexible and robust alternative for modeling skewed and heavy-tailed lifetime data.