Talk:Berry–Esseen theorem

The formula Fn is INCORRECT.

Pls check against the German's page (http://de.wikipedia.org/wiki/Satz_von_Berry-Ess%C3%A9en) or the source already listed in "External links" (Chen, Po-Ning (2002). Asymptotic Refinement of the Berry-Esseen Constant)

The correct one is: Fn = Yn / (standard deviation/sqrt(n))

[Someone else] You are wrong: Fn is cdf of (X1+...+Xn)/(stdev*sqrt(n)) = Yn*sqrt(n)/stdev That's what on the German page you mention, but you read too quickly. —Preceding unsigned comment added by 86.212.95.141 (talk) 09:22, 26 January 2008 (UTC)


 * All three versions of the formula given above are equivalent. (The discussion above has been changed by several anon editors, which is why the "disagreement" no longer makes any sense.) I originally gave the formula in the first form above because that's closer to the way the standardized sample mean is written in introductory statistics textbooks currently used in the U.S. (where I'm from). Some books place the sqrt(n) in the numerator, as in the third form; the second form is talking about the sum, not the mean. - dcljr (talk) 07:52, 16 April 2009 (UTC)

Spelling of Esseen
I claim that the correct spelling of Gustav Esseen's name has no accent on the 'e'. This is a tricky point because it is written with an accent in many sources. He's definitely Swedish; I don't know if this helps determine the truth. Credible citations with no accent:

[]

[]

[] —Preceding unsigned comment added by 67.186.15.220 (talk) 00:39, 26 November 2007 (UTC)
 * I asked to Svante Janson, a former student of Esseen, and a very reliable (among many other qualities) mathematician, about the correct spelling. Here is the answer
 * "Carl-Gustav Esseen" is correct.
 * We also had a professor Matts Essén at the department. (Actually, they were distantly related; different parts of the family adopted different spellings at some time long ago. Esséen is incorrect for both of them.)
 * so we are as close to 100% credible as possible, there. The only question remaining is "is the incorrect spelling so frequent in the literature that the correct spelling would prevent interested readers from finding the article in Wikipedia ?" I think the answer is "no", and that we should rename the article according to the correct spelling very soon.--193.50.42.138 (talk) 16:24, 16 January 2009 (UTC)


 * I agree with this (the original research part notwithstanding ;) and have moved the page. Note that the German article has already been moved to the spelling "Esseen" and their original with the accent deleted. We should keep the accented version as a redirect, however. - dcljr (talk) 08:02, 16 April 2009 (UTC)

X_1 =? X_j
Hi everybody,

Under "Identically distributed summands" it says E(X_1) = mu and E(|X_1|^3) = rho, should that in fact be X_j for j in {1, ..., n}?

Right now it only defines moments for the _first_ variable being summed. Surely this should be for every variable?

Salutacions 88.128.80.6 (talk) 07:29, 17 May 2013 (UTC)


 * If they are "identically distributed", then every Xj has the same distribution (as X1). - dcljr (talk) 08:54, 20 October 2015 (UTC)

External links modified
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 * Added archive https://web.archive.org/web/20040202103426/http://www.stat.unipd.it:80/bernoulli/02a/bn_3.html to http://www.stat.unipd.it/bernoulli/02a/bn_3.html

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 * Seems fine. - dcljr (talk) 23:51, 1 November 2016 (UTC)

Korolev & Shevtsova (2009)
This article currently has several broken links to a missing cite of Korolev & Shevtsova (2009). I'm guessing that these should go to Korolev & Shevtsova (2010), which is cited in the article. That paper seems to have been submitted in 2009 and published in 2010. I am no topical expert, though. Will someone please fix this? Thanks. Wtmitchell (talk) (earlier Boracay Bill) 20:49, 29 September 2018 (UTC)
 * Fixed. Both cited articles for Korolev & Shevtsova were published online in 2010, so I used 2010a and 2010b. - dcljr (talk) 07:12, 16 September 2019 (UTC)

What about when rho is zero
In response to this righteous but unfortunately misguided change, the case where ρ = 0 is impossible given the other conditions on the distribution of X1 (and X2, …, Xn). If ρ = E(|X1|3) = 0, it would imply that X1 is a constant (no variation), but this is prevented by the condition E(X12) = σ2 > 0 (there is positive variation). Certainly E(X13) could be zero, but not E(|X1|3). - dcljr (talk) 06:42, 16 September 2019 (UTC)