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TitleEdgeworth–Cornish–Fisher–Hill–Davis expansions for normal and non-normal limits via Bell polynomials
Publication TypeJournal Article
Year of Publication2015
AuthorsWithers, C.S., and Nadarajah S.
Pagination794 - 805
Date Published2015
ISSN17442508 (ISSN)
AbstractCornish and Fisher gave expansions for the distribution and quantiles of asymptotically normal random variables whose cumulants behaved like those of a sample mean. This was extended by Hill and Davis to the case, where the asymptotic distribution need not be normal. Their results are cumbersome as they involve partition theory. We overcome this using Bell polynomials. The three basic expansions (for the distribution and its derivatives, for the inverse of the quantile, and for the quantile) involve three sets of polynomials. We give new ways of obtaining these from each other. The Edgeworth expansions for the distribution and density rest on the Charlier expansion. We give an elegant form of these as linear combinations of generalized Hermite polynomials, using Bell polynomials. © 2015 Taylor & Francis.

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