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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 29, Fasc. 2,
pages 271 - 280
 

CHARLIER AND EDGEWORTH EXPANSIONS FOR DISTRIBUTIONS AND DENSITIES IN TERMS OF BELL POLYNOMIALS

Christopher S. Withers
Saralees Nadarajah

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: 62E20.

Keywords and phrases: Bell polynomials; Charlier series; Cornish and Fisher.

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