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In this paper the distribution of the sum of independent \(\varGamma \) variables with different scale parameters is obtained by direct integration, without involving a series expansion. One of its particular cases is the distribution of the product of some particular independent Beta variables. Both distributions are obtained in a concise manageable form readily applicable to research work in the area of multivariate statistics distributions. The exact distribution of the generalized Wilks’ \(\varLambda \) statistic is then obtained as a direct application of the results.

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The Generalized Integer Gamma Distribution – A Basis for Distributions in Multivariate Statistics

  • 章节

  • 发表日期：

    2025年

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  • Carlos A. Coelho

摘要

In this paper the distribution of the sum of independent \(\varGamma \) variables with different scale parameters is obtained by direct integration, without involving a series expansion. One of its particular cases is the distribution of the product of some particular independent Beta variables. Both distributions are obtained in a concise manageable form readily applicable to research work in the area of multivariate statistics distributions. The exact distribution of the generalized Wilks’ \(\varLambda \) statistic is then obtained as a direct application of the results.