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Charlier and edgeworth expansions for distributions and densities in terms of bell polynomials

Withers C. S., Nadarajah S.

Probability and Mathematical Statistics

2009

Vol. 29, Fasc. 2

271--280

We show that the coefficients of the Charlier differential series for distributions and densities are simply Bell polynomials in the cumulants. The same is true for the Edgeworth expansions of distributions and densities of sample means. We use this to obtain higher order extensions of these well-known series.