Hi,I'm looking at using the Gram-Charlier or Edgeworth series to parametrise an almost Gaussian distribution.When applying it to N-dimensions (say 2 dimensions here). How would the expansion work so that it maintains its orthogonal function properties? Ideally, I'd like to overlay a copula function.ThanksJohn

Good question. In my library, I see there is some discussion and refs inEx. 6.16 - 6.17, pg 178 of Kendall & Stuart (Adv. theory statistics), Vol I (third edition) They cite this article by Chambers (If you get a copy of the Chambers article, please email me one, as I'd like to see it too)

Hi Alan,I found this... which is along the lines of what I am thinking...www.fe.ualg.pt/conf/mvm/pdf/DelBrio_Nig ... .pdfThanks for your help

Glad you found something useful for you.Personally, what I would like to see would be more along the lines of a standard orthogonal expansion.That is, we expand f(x) = Sum_i c(i) g(i,x), where the g(i,x) = multivariate normal density times some kind of multivariate Hermite(i,x) [x = N-vector, i = multi-index].Then, one gives a formula for the c(i) and you prove convergence with general f(x) within some class of functions that you identify.If anybody sees how to carry this through for N > 1 (and f(x) a density with non-trivial dependencies), please post the development.

Thanks for the link. I looked, but it seems to deal with rotationally symmetric densities. These could beexpanded by the standard 1D Gram-Charlier expansion if their tail behavior was suitable.