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

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  • Coelho, Carlos A.

Abstract

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.

Suggested Citation

  • Coelho, Carlos A., 1998. "The Generalized Integer Gamma Distribution--A Basis for Distributions in Multivariate Statistics," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 86-102, January.
  • Handle: RePEc:eee:jmvana:v:64:y:1998:i:1:p:86-102
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    Citations

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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.
    4. Coelho, Carlos A., 2004. "The generalized near-integer Gamma distribution: a basis for 'near-exact' approximations to the distribution of statistics which are the product of an odd number of independent Beta random variables," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 191-218, May.
    5. repec:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-016-0703-1 is not listed on IDEAS
    6. repec:spr:testjl:v:26:y:2017:i:2:d:10.1007_s11749-016-0512-4 is not listed on IDEAS
    7. Carlos Coelho & Barry Arnold & Filipe Marques, 2015. "The exact and near-exact distributions of the main likelihood ratio test statistics used in the complex multivariate normal setting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 386-416, June.
    8. Arnold, Barry C. & Coelho, Carlos A. & Marques, Filipe J., 2013. "The distribution of the product of powers of independent uniform random variables — A simple but useful tool to address and better understand the structure of some distributions," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 19-36.
    9. Marques, Filipe J. & Loingeville, Florence, 2016. "Improved near-exact distributions for the product of independent Generalized Gamma random variables," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 55-66.
    10. Blacher, René, 2003. "Multivariate quadratic forms of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 2-23, October.

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