Mathematical Properties of a Flexible Lifetime Model with Computational Applications

This study introduces a novel one-parameter probability distribution called the QGamma distribution (QGaD), constructed through a specific mixture of the exponential and Chris–Jerry distributions. The mathematical properties of the QGaD are thoroughly investigated, including its probability density function, cumulative distribution function, moments, variance, mean residual life function, order statistics, and hazard rate function. Fifteen classical estimation methods are employed to estimate its parameter, with their performance evaluated through a Monte Carlo simulation. The flexibility and modeling capability of the proposed distribution are assessed by comparing it with several well-known distributions, including the exponential, Chris–Jerry, gamma, sine exponential, Shanker, Lindley, and X-Lindley distributions. The empirical results reveal that the QGaD provides superior fits to real-world data based on standard goodness-of-fit measures. Overall, the findings highlight the potential of the QGaD as a robust and flexible tool for modeling lifetime and reliability data. The study concludes that QGaD makes a valuable contribution to the development of statistical models, particularly in contexts that require a parsimonious yet versatile distribution.