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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
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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.
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- Copyright © Institute of Actuaries Students' Society 1947