This study introduces the Hooriya Shah Gamma Distribution, a novel extension of the classical Gamma distribution designed to provide greater flexibility in modeling skewed and non-negative data. The proposed distribution incorporates an additional parameter to improve adaptability in capturing diverse data behaviors observed in real-world applications, particularly in reliability analysis, survival studies, and financial modeling. Key statistical properties of the distribution, including probability density function, cumulative distribution function, moments, hazard function, and parameter estimation methods, are derived and discussed in detail. Parameter estimation is performed using maximum likelihood estimation, and the performance of the model is evaluated through simulation studies. The applicability of the Hooriya Shah Gamma Distribution is demonstrated using three real datasets, where it is compared with existing distributions. Results indicate that the proposed model provides a better fit and enhanced modeling capability, making it a valuable contribution to statistical theory and applied data analysis.
Keywords: Alamgir Gamma distribution, Gamma Distribution, Simulation Study, maximum likelihood estimation; hazard function, model fitting
