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IV.—A Note on Karl Pearson's Selection Formulæ

Published online by Cambridge University Press:  14 February 2012

D. N. Lawley
D. N. Lawley
Affiliation:
Moray House, University of Edinburgh
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Extract

It is a well-known fact that Karl Pearson's formulae expressing the effect of selection on the means, variances and covariances of a multivariate population hold when the variates are such as to be normally distributed both before and after selection. It is not, however, generally known that the formulae are true under much more general conditions, and in view of a recent controversy it has been thought desirable to establish precisely what these conditions are. In dealing with the problem we shall adopt the shortened vector and matrix notation introduced by Aitken (I). This notation is reproduced below with but slight modifications.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 62 , Issue 1 , 1944 , pp. 28 - 30
Copyright
Copyright © Royal Society of Edinburgh 1944

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References

REFERENCE TO LITERATURE

Aitken, A. C., 1934. “Note on Selection from a Multivariate Normal Population,” Proc. Edin. Math. Soc., IV, 106–110.Google Scholar