Talk:Illustration of the central limit theorem

message: For what it's worth, it occurs to me (1) figures with the probability curves in red (with black or gray for the box) would "read" better, and (2) it could be nice to post some lines of Octave so that people can "try it at home". I'm sure there are other ways to improve this page. I'll get around to the stuff above eventually. Wile E. Heresiarch 02:41, 6 Apr 2004 (UTC)
thread_title:  Error on the page! 

message: The article Concrete illustration of the central limit theorem appears to me to be a spinoff with insufficient substance for being an independent article.  --LambiamTalk 17:34, 12 April 2007 (UTC)
replies: text: Maybe it's a POV fork. 193.95.165.190 12:46, 1 August 2007 (UTC)

text: I say, merge and change the name to Demonstrations of the central limit theorem or something like that.  I rather like the discrete illustration given here as it is easier for beginners to see than the example with the continuous (or rather, piecewise continuous) distribution. VectorPosse 08:41, 27 August 2007 (UTC)
thread_title:  Merge proposal 

message: The Java applet on dice throwing does not demonstrate the central limit theorem. 
Instead, it demonstates a form of the law of large numbers (which, roughly stated, 
asserts that observed frequencies converge almost surely to 
probabilities as the sample size increases without bound). Note that
the limiting distribution in each case of the applet is not a normal distribution;
instead it is the distribution of total spot numbers for the particular case of dice
tossing (which is only approximately normal when several dice are tossed). 
[by Marvin Ortel, on 2:14PM 11 November 2007, Honolulu, Hawaii]
:I disagree. It's a valid demonstration of the CLT. The convergence to normality can be seen by going from 1 dice to 5, which gives a similar progression as in this article. Birge (talk) 20:49, 19 December 2007 (UTC)
thread_title:  Error on the page! 

message: The final short section, "Probability mass function of the sum of 1,000 terms" has an error in either the text or the figure. The figure shows a histogram of a sample with a mean around 2000. However the expected sum of 1000 *standard* ([0,1]) uniform samples should be around 500. If the draws are coming from a [0,4] uniform distribution then the histogram should display larger variance. The histogram looks much more like the distribution of the sum of 4000 standard uniform samples.  — Preceding unsigned comment added by 128.135.100.102 (talk) 18:33, 19 January 2012 (UTC)
replies: text: It's a question of interpretation. My interpretation is that, given that the subsection is part of the "discrete distribution" section, both the "uniform distribution" and the "example on this page" are referring to the 3-point equal-probability discrete distribution on the values 1,2,3 that is used at the start of the section. If this is what is actually meant, then the text and/or figure caption just needs to be clarified. Melcombe (talk) 22:24, 19 January 2012 (UTC)
thread_title:  Error on the page! 

message: The illustration and discussion of the continuous case is not optimal in my opinion. The CLT alone does not guarantee that the sequence of densities converges pointwise to the normal density, but the illustration and discussion in this article could be easily misinterpreted in this way. Since this is a common misconception of the CLT, I would suggest to make this point clearer and at least note that what is shown in the illustration (pointwise convergence of the density) is an actually stronger type of convergence than convergence in distribution. The current illustration would be better suited for an article on local limit theorems.
For this article, I think it would be better to plot histograms instead of densities plus the density of the standard normal distribution and describe in the text that the area of each bar of the histogram converges to the area in that interval under the normal density. This would be closer to the actual content of the CLT.
--Zakoohl (talk) 12:27, 6 June 2021 (UTC)
thread_title:  Is the illustration in the continuous case really optimal?