Note on the derivation of fluctuation formulae for statistical assemblies
Published online by Cambridge University Press: 24 October 2008
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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