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The generalised product moment distribution in a normal system

Published online by Cambridge University Press:  24 October 2008

J. Wishart  and
M. S. Bartlett
J. Wishart
Affiliation:
Clare College
M. S. Bartlett
Affiliation:
Queens' College
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Extract

1. In a previous paper (1) the authors used the theory of the moment generating function to deduce the known random sampling distributions of the estimated variance and co-variance in a system of variables following the normal law of frequency. In this paper we shall go much further. By means of the same general method the simultaneous distribution of the ½p (p + 1) second order moment statistics in a normal system of p mutually correlated variables will be deduced. It will be shown to be completely independent of that of the p sample means, and incidentally the method of proof to be developed will be found, in the special cases p = 1 and 2, to be an improvement on that given in the earlier paper, being independent of previous results reached by other authors.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 29 , Issue 2 , May 1933 , pp. 260 - 270
Copyright
Copyright © Cambridge Philosophical Society 1933

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References

REFERENCES

(1)Wishart, J. and Bartlett, M. S., Proc. Camb. Phil. Soc., 28 (1932), 455–459.CrossRefGoogle Scholar
(2)Aitken, A. C., Quart. Journ. Math., 2 (1931), 130–135.CrossRefGoogle Scholar
(3)Fisher, R. A., Biometrika, 10 (1915), 507–521.Google Scholar
(4)Romanovsky, V., Metron, 5, no. 4 (1925), 3–46 (32).Google Scholar
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(6)Wishart, J., Biometrika, 20 A (1928), 32–52.CrossRefGoogle Scholar