A mixed gamma distribution model: Theoretical insights and applications to medical data

Abstract

This paper proposes a novel mixed gamma distribution (NMGD) and systematically investigates its statistical properties, including moments, shape parameters, coefficient of variation, moment-generating function, survival function, and hazard function. Parameter estimation is addressed using both the method of moments and maximum likelihood estimation. The practical utility of the NMGD is demonstrated through applications to three empirical datasets: (i) recovery times (in minutes) for patients administered pain relievers, (ii) recovery durations (in months) for breast cancer patients treated with Trastuzumab, and (iii) monthly tax revenue data from Egypt spanning 59 months. Goodness-of-fit is evaluated using the Kolmogorov-Smirnov test, while model selection is guided by Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC). The results indicate that the NMGD provides a superior fit compared to conventional distributions across all datasets, underscoring its potential as a flexible and robust model for medical and financial data analysis.