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The distribution of second order moment statistics 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

Let x be a normally distributed variable, which may without loss of generality be measured from the mean of the distribution, so that E(x) = 0, E denoting mathematical expectation. Then x satisfies the differential relation

where k2 (otherwise σ2 or (2h2)−1) is the semi-invariant of order 2. Also k1 = 0, and we know that kr = 0 for r > 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 4 , October 1932 , pp. 455 - 459
Copyright
Copyright © Cambridge Philosophical Society 1932

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References

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