Talk:Chi-squared distribution

message: The current notation has F_x and other symbols that are no defined.  —Preceding unsigned comment added by Wilgamesh (talk • contribs) 17:28, 7 August 2009 (UTC)
thread_title:  clean up derivation of 1 parameter pdf 

message: I just came here looking for the history of Chi-Squared, credit for initial development, historical context, time line, rise in popularity, etc.  I think a growing criticism of wikipedias math treatment is an inconsistant voice about whether or not it wants to be a technical encyclopedia or have elements of the history of the math.  It probably needs both for completeness; however, in this case the article is sharply skewed in the technical direction with very little historical merit.
72.200.80.12 15:33, 3 June 2007 (UTC)
thread_title:  needs historical treatment 

message: "If Xi are k independent, normally distributed random variables with mean 0 and variance 1..."
Does it mean that X1 is a normal variable whose mean is 0 variance is 1, X2 is a normal variable whose mean is 0 and variance is 1, etc, or does it mean that if you looked at all k of the variables, their collective mean is 0 and variance is 1, or does it necessarily imply both meanings?  I'm confused because I am accustomed to being told that we have a single variable X that we sample k observations of, not a whole bunch of different variables at once. 207.189.230.42 (talk) 07:16, 8 June 2009 (UTC)
replies: text: There is no such thing as a "collective mean"; the mean is a property of a single random variable. Your first interpretation is correct, with the additional information that the different variables are also independent. --Zvika (talk) 07:41, 8 June 2009 (UTC)
thread_title: What does this sentence mean to tell me?

message: I suggest that we change the notation for chi² distribution from \chi^2_k\, to \chi^2(k)\, (both of them can be encountered in the literature). The reason for such change is to have more uniform notation for different distributions across the Wikipedia: <name of distribution>(<parameters>). For example, we have N(μ,σ2) for normal, Poisson(λ) for Poisson, F(k1,k2) for F-distribution, Binomial(n,p) for binomial, etc. Such notation is also more convenient to display in-line using HTML: χ2(k).  … stpasha »  20:54, 29 November 2009 (UTC)
replies: text: I think either is OK, but the change will have to be in the entire article. --Zvika (talk) 07:01, 30 November 2009 (UTC)

text: I have seen d, k, v, f (and obviously n, m etc when there's more than one) used for the degrees of freedom. I can't really tell which is the most common. --Paulginz (talk) 20:24, 22 July 2010 (UTC)
thread_title:  Notation 

message: Regarding the central limit theorem, the article makes the assertion
:k > 50 is “approximately normal”
I don't know if this is a quote from the source or what but, regardless, the statement needs to be qualified in some fashion. Any value of of k could be considered "approximately normal" depending on how one defines that. What is the criterion being applied to make this assertion?
--Mcorazao (talk) 20:37, 4 May 2010 (UTC)
thread_title:  Approximately normal 

message: how to find it? 174.91.224.96 (talk) 18:21, 28 November 2010 (UTC)
thread_title: Skewness

message: I feel that it is very important to mention scaled chi square distribution. Suppose Y is chi square with df k, what is the distribution of cY where c>0??? Jackzhp (talk) 03:21, 5 January 2011 (UTC)
thread_title: Scaled Chi square distribution

message: suppose Y has chi square distribution, what is the distribution of log(Y)? Jackzhp (talk) 02:51, 9 February 2011 (UTC)
thread_title: Log

message: The assertion that
If X_i \sim \mathrm{Laplace}(\mu,\beta)\, then \sum_{i=1}^n{\frac{2}{\beta|X_i-\mu|}} \sim \chi^2(2n)\,
seems unlikely.  In fact,  {\frac{2|X_i-\mu|}{\beta}} \sim \chi^2(2)\,,
so it seems far more likely that \sum_{i=1}^n{\frac{2|X_i-\mu|}{\beta}} \sim \chi^2(2n)\,.
Primrose61 (talk) 22:42, 18 October 2011 (UTC)
thread_title:  Connection with Laplace distribution 

message: The graph shows that CDF at   for .
--Yecril (talk) 14:34, 24 March 2012 (UTC)
thread_title:  CDF graph is wrong 

message: In the subsection "Gamma, exponential, and related distributions", the first sentence refers to "the shape parameterization of the gamma distribution".  If one visits the wikipedia page for the gamma distribution, all three parameterizations contain a "shape" parameter.  Hence, referring to the "shape parameterization" does nothing to disambiguate the parameterization being referred to here.
Craniator (talk) 01:58, 18 March 2013 (UTC)
thread_title:  Ambiguous reference to "shape parameterization of the gamma distribution" 

message: I think somebody meant to change the CDF, but changed the graph for the PDF, instead.  — Preceding unsigned comment added by 171.67.87.31 (talk) 23:48, 26 April 2013 (UTC)
thread_title:  The probability distribution graph is wrong, now 

message: This article literally makes no sense to me. I'm wondering if I can decode even a single sentence or equation. It is written as if the reader already knows much about the distribution. As it stands, you need a bachelors in math just to figure out what the article is saying. ~EDDY (talk/contribs)</span>~ 14:03, 1 July 2014 (UTC)
thread_title:  Needs work 

message: The article stated: 
:If Y is a vector of k i.i.d. standard normal random variables and A is a k×k idempotent matrix with rank k−n then the quadratic form YTAY is chi-squared distributed with k−n degrees of freedom.
I've added the necessary condition that A be symmetric.  I get the impression that most experts would have assumed this from the fact that we have a quadratic form, but making this requirement explicit will help beginners.  BTW, a counter-example to the theorem as originally stated would be: A=\begin{bmatrix}1 & 1 \\ 0 & 0 \end{bmatrix}, which is idempotent and leads to $Y_1^2+Y_1 Y_2$ which is not Chi-squared since it could potentially take on negative values.  — Preceding unsigned comment added by Monsterman222 (talk • contribs) 20:44, 1 October 2014 (UTC)
thread_title: Made property more explicit

message: Please add to the article … what is the exact median of the χ2 distribution for the first few integer values for degrees of freedom?  104.129.194.123 (talk) 17:55, 11 June 2015 (UTC)
thread_title:  Medians missing 

message: In the "Relation to other distributions" section, the first entry gives the limit as k\to\infty. What does the arrow with the d on top \left(\xrightarrow{d}\right) mean? It's not obvious to me. MystRivenExile (talk • contribs) 15:39, 22 August 2016 (UTC)
thread_title:  Arrow notation 

message: Second paragraph. First sentence. I'm not sure what the author intended from this word. Perhaps something related to statistical independence since the first portion of this word links to an article on statistical independence. (indeution)
Bradybray (talk) 17:08, 14 June 2017 (UTC)
thread_title: Mistake in Intro

message: "Pronounced like chai tea, the chi-square,"
I think this is:
1) Wrong; and
2) Unhelpful.
1) The Greek letter chi starts with a 'k' sound, while chai tea starts with a 'ch' sound.
2) One unfamiliar foreign word is being illustrated with another unfamiliar foreign word?!
GeneCallahan (talk) 16:07, 29 June 2017 (UTC)
thread_title:  Pronounciation 

message: Due to the page being moved unexpectedly and without discussion, the following is now featured on the About page part of Talk:
"Chi-square distribution has been listed as a level-5 vital article in an unknown topic'".
The page should be moved back to Chi-squared distribution, there was no consensus to move it. Кирилл С1 (talk) 10:41, 27 May 2020 (UTC)
replies: text: It was equally broken before the move.  I added the topic=Mathematics to fix it (I think). Dicklyon (talk) 07:03, 7 September 2020 (UTC)
thread_title:  Moving page without consensus 

message: I see in the "definitions > introduction" section the 3 lines hereunder that seems to be wrong.
: \chi^2 = {(m - Np)^2\over Npq} 
:Using N = Np + N(1 - p), N = m + (N - m), and q = 1 - p, this equation can be rewritten as
: \chi^2 = {(m - Np)^2\over Np} + {(N - m - Nq)^2\over Nq} 
I would suggest to replace these lines with lines hereunder and also to use Z in place of χ²  :
: Z^2 = {(m - Np)^2\over Npq}  as Z is the usual letter used for a standard normal distribution
:Using 1 = p + q  , this equation can be rewritten as
: Z^2 = { ( p + q ) (m - Np)^2\over Npq} = {(m - Np)^2\over Np} + {(m - Np)^2\over Nq} 
BUT <B>more important is that this part of the introduction has no sense</B> as it is the Cochran's theorm that shows that variable hereunder has a χ² distribution 
:D = \sum_{i=1}^n \frac{(O_i - E_i)^2}{E_i}  
So I would recommend to suppress these very confusing lines and just replace them by a link to the Cochran's theorm
Regloor (talk) 13:47, 15 June 2021 (UTC)
thread_title:  error in the "definitions > introduction" section ? 

message: In what way is the chi square a special case of the gamma distribution? If the special case is defined by setting the gamma didtribution rate parameter beta to 0.5 this ought to be clearly stated.150.227.15.253 (talk) 19:39, 15 December 2022 (UTC)
thread_title:  Special case? 

message: I am not sure we should have a PGF (probability generating function) in the infobox for a continuous distribution.  It is actually a factorial moment generating function but if you understand that then you probably also understand that it is a simple adaptation of the moment generating function [take log(t)] and so do not need it stated in addition to the MGF. 193.240.203.36 (talk) 16:12, 18 May 2023 (UTC)
thread_title:  Probability generating function