Talk:Edgeworth series

From Wikipedia, the free encyclopedia

This article is within the scope of WikiProject Statistics, which collaborates to improve Wikipedia's coverage of statistics. If you would like to participate, please visit the project page.
WikiProject Mathematics
Mathematics Portal
This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating: Start Class Mid Priority  Field: Probability and statistics

In this article as it originally appeared, the statement of the central limit theorem was wrong. The error was copied from the cited 1958 paper. Here is a simple counterexample: Suppose X1 = 0 or 1, each with probability 1/2, and Xi = 0 with probability 1. Then the expression that was asserted to approach the normal c.d.f. does not. I have inserted the additional hypothesis that the sum of the variances diverges to infinity. Michael Hardy 02:34, 10 May 2004 (UTC)


I have changed f(x) to F(x) in the statement about the convergence at the end of the Gram-Charlier A series. I think that is the function which was meant. Lafrontera 17:51, 10 February 2007 (UTC)

I changed the priority to mid because (1) Edgeworth expansions are taught first or second term in the core of a stats PhD; (2) they are also taught to some masters students; and, (3) they are used in other fields (such as astronomy). Someday soon I'll update the page for the general form of the expansion. --Cumulant 20:55, 21 August 2007 (UTC)

[edit] Gram-Charlier

Who are they? Albmont 17:02, 27 July 2007 (UTC)

Good question. I'm not sure, but I suspect Gram is the same person whose name appears in the phrase Gram-Schmidt process, and that Charlier is the one whose name appears in Poisson-Charlier polynomials. Michael Hardy 21:21, 27 July 2007 (UTC)
Gram is the same; suspect (but haven't confirmed) that Charlier is also the same. FWIW, Gram and Charlier were mathematicians living around the end of the nineteenth century. The Gram-Charlier Series was actually found first by Thiele who gets no credit (thus partially fulfilling Stigler's law of eponymy).
Thiele's work was published in 1871 as (Danish) "En mathematisk Formel for Dødeligheden, prøvet paa en af Livsforsikringanstalten af 1871 benyttet Erfaringrække"; an English translation followed in 1872. Gram's article was published in 1883 as (German) "Über die Entwickelung reeler Funktionen in Reihen mittelstder Methode der kleinsten Quadrate". Charlier? Eh. Late to the party from what I can tell -- although if someone can figure out how he enters in, I'd love to hear it.--Cumulant 19:32, 15 August 2007 (UTC)