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Note on the derivation of fluctuation formulae for statistical assemblies

Published online by Cambridge University Press:  24 October 2008

M. S. Bartlett
M. S. Bartlett
Affiliation:
Queens' College
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Extract

1. A familiar device in the study of statistical distributions is to form the moment-generating function

where the bar denotes averaging over all values of the statistical variate x. The moments μr of x are the coefficients of αr/r!, and the derived coefficients in the expansion of K ≡ log M are termed the semi-invariants kr. In particular,

and, for the normal (Gaussian) law,

we have the simple formula

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 33 , Issue 3 , July 1937 , pp. 390 - 393
Copyright
Copyright © Cambridge Philosophical Society 1937

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References

REFERENCES

(1)Fowler, R. H.Statistical mechanics, 2nd ed. (Cambridge, 1936.)Google Scholar
(2)Wishart, J. and Bartlett, M. S.Proc. Camb. Phil. Soc. 29 (1933), 260–70.CrossRefGoogle Scholar