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The arithmetical character of the Wishart distribution

Published online by Cambridge University Press:  24 October 2008

Paul Lévy
Paul Lévy
Affiliation:
École PolytechniqueParis
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Extract

Let ξ and η be two independent and normal random variables, with zero means and with standard deviations each equal to ½ Put

The joint distribution of X, Y, Z is a particular case of the Wishart distribution (1). It may be defined by the generating function of its cumulants (c.g.f.)

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 2 , April 1948 , pp. 295 - 297
Copyright
Copyright © Cambridge Philosophical Society 1948

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References

REFERENCES

(1)Wishart, J.Biometrika, 20a (1928), 32.CrossRefGoogle Scholar
(2)Lévy, P.Bull. Sci. Math. 63 (1939), 247.Google Scholar
(3)Lévy, P.Théarie de l'addition des variables aléatoires (Paris, 1937), no. 54.Google Scholar
(4)Doetsch, G.Math. Z. 40 (1935), 613 (622).CrossRefGoogle Scholar
See also Lévy, P.Compositio Mathematica, 7 (1939), 283 (284, 290–4).Google Scholar