CHARLIER AND EDGEWORTH EXPANSIONS FOR DISTRIBUTIONS AND
DENSITIES IN TERMS OF BELL POLYNOMIALS
Christopher S. Withers
Abstract: 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.
2000 AMS Mathematics Subject Classification: Primary: 62E17; Secondary:
Keywords and phrases: Bell polynomials; Charlier series; Cornish and Fisher.