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Proof of the distributions of X2, of the estimate of variance, and of the variance ratio

Published online by Cambridge University Press:  11 August 2014

John Wishart
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Extract

In the discussion on the paper ‘The Variance Ratio test in Statistics’, given to the Students' Society on 13 December 1946, and printed in J.S.S. Vol. VI (1947), p. 172, the desire was expressed for a proof by relatively elementary methods of the distribution of the variance ratio. As such a proof must first derive the distribution of X2 modified into that of a variance estimate, three distributions are involved (in addition to that of the sample mean). The various steps are given in this paper. A note is added on the probability integral of the variance ratio distribution.

Type
Research Article
Information
Journal of the Staple Inn Actuarial Society , Volume 7 , Issue 2 , October 1947 , pp. 98 - 103
Copyright
Copyright © Institute of Actuaries Students' Society 1947

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References

(1) Weatherburn, C. E. A first course in Mathematical Statistics (1946). Cambridge University Press.Google Scholar
(2) Tables of the Incomplete Beta Function. Edited by Pearson, Karl (1934). London: ‘Biometrika’ Office.Google Scholar
(3) Biometrika (1941), Vol. XXXII, p. 168.Google Scholar
(4) Fisher, R. A. & Yates, F. Statistical Tables (1938, 1943). Oliver and Boyd.Google Scholar