Derivation of The Generalized Gamma DistributionVia An ‎Ordinary Differential Equation Approach: Theory and Applications

  • Authors

    • Mohammad Shakil Department of Mathematics, Miami Dade College, Hialeah, FL, USA
    • Tassaddaq Hussain Department of Statistics, Mirpur University of Science and Technology, Mirpur, Pakistan
    • Mohammad Ahsanullah Department of Management Sciences, Emeritus Professor, Rider University, NJ, USA
    • B. M. G. Kibria Dept. of Math & Stat, Florida International University, FL, USA
    https://doi.org/10.14419/3b25xq49

    Received date: August 6, 2025

    Accepted date: November 3, 2025

    Published date: November 8, 2025

  • Characterization; Differential Equation; Generalized Gamma Distribution; Truncated Moment

  • Abstract

    This paper introduces a novel approach for generating the Generalized Generalized Gamma (GGG) ‎distribution by employing a second-order non-homogeneous non-linear differential equation with ‎constant coefficients. The proposed framework yields a flexible univariate continuous probability ‎distribution with a rich structure. We provide a comprehensive analysis of the distribution’s ‎formulation, key statistical properties, and characterizations via truncated moments. Parameter ‎estimation is carried out through both the Maximum Likelihood Estimation (MLE) and the Method of ‎Moments. A simulation study is conducted to assess the performance of these estimators. The ‎practical applicability of the GGG distribution is demonstrated using real-life datasets, with model ‎adequacy evaluated through multiple goodness-of-fit criteria, including the Anderson-Darling and ‎Cramér–von Mises tests. The empirical results highlight the superior performance of the proposed ‎distribution in modeling complex data patterns. Findings and implications are thoroughly discussed, ‎underscoring the GGG distribution’s potential in statistical modeling and applied probability‎.

    Author Biography

    • Mohammad Shakil, Department of Mathematics, Miami Dade College, Hialeah, FL, USA

      Liberal Arts and Sciece Department (Mathematics), Professor

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