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<p>The Gauss hypergeometric (GH) distribution encompasses several notable distributions such as the beta, generalized three parameter beta, Topp-Leone, power function and uniform distributions. In this paper, we obtain a characterization of GH distribution and propose a new goodness-of-fit test based on this characterization. We use U-statistic theory to obtain the test statistic and study its properties. To evaluate the performance of the proposed test, Monte Carlo simulations are conducted. Finally, we demonstrate the practical applicability of the test through four real-world datasets, highlighting its effectiveness across various contexts.</p>

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Goodness-of-Fit Test for Gauss Hypergeometric Distribution: A Unified Framework for Topp-Leone and Generalized Beta Distributions

  • 期刊论文

  • 发表日期：

    2025年7月30日

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  • P B Amjish,
  • K Jayakumar

摘要

The Gauss hypergeometric (GH) distribution encompasses several notable distributions such as the beta, generalized three parameter beta, Topp-Leone, power function and uniform distributions. In this paper, we obtain a characterization of GH distribution and propose a new goodness-of-fit test based on this characterization. We use U-statistic theory to obtain the test statistic and study its properties. To evaluate the performance of the proposed test, Monte Carlo simulations are conducted. Finally, we demonstrate the practical applicability of the test through four real-world datasets, highlighting its effectiveness across various contexts.