http://www.johndcook.com/blog/2008/09/30/quantifying-the-error-in-the-central-limit-theorem/ The blog of John D. Cook Fri, 19 Mar 2010 05:39:36 -0400 http://wordpress.org/?v=2.8.4 hourly 1 http://www.johndcook.com/blog/2008/09/30/quantifying-the-error-in-the-central-limit-theorem/comment-page-1/#comment-10435 John Mon, 01 Dec 2008 22:10:41 +0000 http://www.johndcook.com/blog/?p=419#comment-10435 Patrick: I'm not aware of a result like you're looking for. I suspect you may not find one. The Berry-Esseén theorem is very general, and so it's often pessimistic in specific applications, and apparently not too much has been published for more particular cases. You might try the book I linked to above. Maybe it would point you to a useful reference. Sorry I couldn't be more help. Patrick: I’m not aware of a result like you’re looking for. I suspect you may not find one. The Berry-Esseén theorem is very general, and so it’s often pessimistic in specific applications, and apparently not too much has been published for more particular cases. You might try the book I linked to above. Maybe it would point you to a useful reference. Sorry I couldn’t be more help.

]]> http://www.johndcook.com/blog/2008/09/30/quantifying-the-error-in-the-central-limit-theorem/comment-page-1/#comment-10432 Patrick Mon, 01 Dec 2008 20:48:44 +0000 http://www.johndcook.com/blog/?p=419#comment-10432 I am looking for a refinement of the Berry-Esseen constant when the initial distribution has some "good" properties. In my specific case, I'd like to use the Berry-Esseen theorem with a histogram distribution. Using the standard approximation (C=0.75) yields a relative error of 0.05 ; while a simulation shows a relative error of less than 0.001. Are you aware of such a result ? Thanks in advance. I am looking for a refinement of the Berry-Esseen constant when the initial distribution has some “good” properties. In my specific case, I’d like to use the Berry-Esseen theorem with a histogram distribution. Using the standard approximation (C=0.75) yields a relative error of 0.05 ; while a simulation shows a relative error of less than 0.001. Are you aware of such a result ? Thanks in advance.

]]> http://www.johndcook.com/blog/2008/09/30/quantifying-the-error-in-the-central-limit-theorem/comment-page-1/#comment-7588 The 41st Carnival of Mathematics « 360 Fri, 10 Oct 2008 23:31:07 +0000 http://www.johndcook.com/blog/?p=419#comment-7588 [...] assume a sufficiently large number of samples. John Cook, from The Endeavor, wants to know about quantifying the error in the central limit theorem, and how close an approximation we can really get. He also compares three methods of computing [...] [...] assume a sufficiently large number of samples. John Cook, from The Endeavor, wants to know about quantifying the error in the central limit theorem, and how close an approximation we can really get. He also compares three methods of computing [...]

]]> http://www.johndcook.com/blog/2008/09/30/quantifying-the-error-in-the-central-limit-theorem/comment-page-1/#comment-7217 Peter Wed, 01 Oct 2008 08:49:15 +0000 http://www.johndcook.com/blog/?p=419#comment-7217 The links to the distribution families don't work. These seem to be the correct ones: <a href="http://www.johndcook.com/normal_approx_to_beta.html" rel="nofollow">beta</a> <a href="http://www.johndcook.com/normal_approx_to_binomial.html" rel="nofollow">binomial</a> <a href="http://www.johndcook.com/normal_approx_to_gamma.html" rel="nofollow">gamma</a> <a href="http://www.johndcook.com/normal_approx_to_poisson.html" rel="nofollow">Poisson</a> <a href="http://www.johndcook.com/normal_approx_to_t.html" rel="nofollow">t</a> The links to the distribution families don’t work. These seem to be the correct ones:
beta
binomial
gamma
Poisson
t

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