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


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  • Coelho, Carlos A.
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    In this paper the distribution of the sum of independent[Gamma]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'[Lambda]statistic is then obtained as a direct application of the results.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 64 (1998)
    Issue (Month): 1 (January)
    Pages: 86-102

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    Handle: RePEc:eee:jmvana:v:64:y:1998:i:1:p:86-102

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    Keywords: independent Gamma variables different scale parameters integer shape parameters independent Beta variables Wilks' Lambda likelihood ratio statistic;


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    Cited by:
    1. Filipe Marques & Carlos Coelho, 2013. "Obtaining the exact and near-exact distributions of the likelihood ratio statistic to test circular symmetry through the use of characteristic functions," Computational Statistics, Springer, vol. 28(5), pages 2091-2115, October.
    2. Das, Sourish & Dey, Dipak K., 2010. "On Bayesian inference for generalized multivariate gamma distribution," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1492-1499, October.
    3. Carlos Coelho & Filipe Marques, 2012. "Near-exact distributions for the likelihood ratio test statistic to test equality of several variance-covariance matrices in elliptically contoured distributions," Computational Statistics, Springer, vol. 27(4), pages 627-659, December.


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