Moments from cumulants and vice versa

Authors: Withers, Christopher1; Nadarajah, Saralees2

Source: International Journal of Mathematical Education in Science and Technology, Volume 40, Number 6, January 2009 , pp. 842-845(4)

Publisher: Taylor and Francis Ltd

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Abstract:

Moments and cumulants are expressed in terms of each other using Bell polynomials. Inbuilt routines for the latter make these expressions amenable to use by algebraic manipulation programs. One of the four formulas given is an explicit version of Kendall's use of Faa di Bruno's chain rule to express cumulants in terms of moments.

Keywords: Bell polynomials; cumulants; Faa di Bruno's chain rule; moments

Document Type: Research article

DOI: 10.1080/00207390902971957

Affiliations: 1: Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand 2: School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

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