A Multivariate Gamma Type Distribution Whose Marginal Laws are Gamma, and which has a Property Similar to a Characteristic Property of the Normal Case

  • A. Dussauchoy
  • R. Berland
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 17)


Reasoning by analogy with a characteristic property of the multivariate normal distribution, we give here a distribution with marginal laws which have the same property as the characteristic property of the normal law. This distribution has one dimensional marginal laws which are gamma laws.

Key Words

Multivariate gamma multivariate normal 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Berland, R. and Dussauchoy, A. (1973). Aspects statistiques des régimes de micro-décharges électriques entre electrodes métalliques placées dans le vide industriel. VACUUM.Google Scholar
  2. [2]
    Bondesson, L. (1973). Z. Wahrschein Verw. Geb. 26, 335–344.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    Bruce, M., et al. (1972). Amer. Statist. Assoc. 67, 927–929.zbMATHCrossRefGoogle Scholar
  4. [4]
    Cramer, H. (1963). Mathematical Methods of Statistics. Princeton University Press.Google Scholar
  5. [5]
    David, F. N. and Fix, E. (1961). In Proceedings of the Fourth Berkeley Symposium, Vol. 1. University of California Press, pp. 177–197.Google Scholar
  6. [6]
    Dussauchoy, A. and Berland R. (1972). Lois gamma a deux dimensions. CRAS Paris T 274 série A, 1946–1949.MathSciNetzbMATHGoogle Scholar
  7. [7]
    Griffiths, P. C. (1969). The canonical correlation coefficients of bivariate gamma distribuionns. Ann. Math. Statist. 40.Google Scholar
  8. [8]
    Kibble, W. F. (1945). An extension of theorem of Mehler on Hermite polynomials. Proc. Cambridge Phil. Soc. 41.Google Scholar
  9. [9]
    Krishnamoorthy, A. S. and Parthasarathy, M. (1951). Ann. Math. Statist. 22, 549–557.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    Mathai, A. M. (1972). Products and ratios of generalized gamma variate. Skandin. Aktuarietidskrift, pp. 194–198.Google Scholar
  11. [11]
    Stacy, E. W. (1962). Ann. Math. Statist. 33, 1187–1192.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht-Holland 1975

Authors and Affiliations

  • A. Dussauchoy
    • 1
    • 2
  • R. Berland
    • 1
    • 2
  1. 1.Université Lyon IVilleurbanneFrance
  2. 2.LimogesFrance

Personalised recommendations