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Note on Selection from a Multivariate Normal Population

Published online by Cambridge University Press:  20 January 2009

A. C. Aitken
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The problem of statistical “selection” is concerned with the alteration induced in a frequency distribution in several variables by an alteration of the parameters in a subsection of the distribution. It may be illustrated by a simple trivariate case, as follows:

From a population characterised by variables x, y, z, correlated and normally distributed, with means 0, 0, 0, variances and product variances r12σ1σ2, r13σ1σ3, r23σ2σ3, a sub-population is extracted by selection in x alone, in such a way that after selection x is still normally distributed, but with mean h and variance s2 . It is required to determine the new values, in the selected population, of the means and variances of y and z, and of the product variances.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 4 , Issue 2 , January 1935 , pp. 106 - 110
Copyright
Copyright © Edinburgh Mathematical Society 1935

References

REFEEENCES

1.Pearson, K.Phil. Trans. Boy. Soc., London, 200 A (1902), 1–66.Google Scholar
2.Soper, H. E., Frequency Arrays (Cambridge, 1922), 20–21.Google Scholar