Talk:Quantile function

I have started to add some material to this page, focusing on providing basic refs for the Normal and Student case. First additions done April 19 2007, with more to come - WSShaww 09:43, 19 April 2007 (UTC)

Added ref to Gilchrist book April 23, Shaww 09:41, 23 April 2007 (UTC)

Added link to quantile page Shaww 16:45, 23 April 2007 (UTC)

Shouldn't this article mention somewhere that the integral of the quantile gives the expected value? —Preceding unsigned comment added by 142.161.241.193 (talk) 18:33, 24 October 2008 (UTC)

Definition
In "All of Statistics" by Larry Wasserman (page 25), $$Q(p)$$ is defined as $$Q(p)\,=\,\inf\left\{ x\in R : p < F(x) \right\}$$ for $$p \in [0,1]$$. The inequality is strict and $$p$$ can be equal to $$0$$ or $$1$$. Is it nevertheless correct ? — Preceding unsigned comment added by 90.46.252.14 (talk) 13:00, 24 February 2013 (UTC)


 * Inequality strict: Sadly, this matters. If F is constant in the interval [x1,x2], and strictly increasing right before and after, and F takes the value p0 in this interval, then {x:p0<F(x)} = (x2,\infty) while {x:p0<=F(x) = [x1,\infty). I would go with the definition given here. I do not know why Larry did not use this definition.
 * Allowing p to be 0,1: This article also allows this and should be fine. But with the definition in this book, Q(1) = infty no matter the distribution.
 * For an empirical distribution with data x1<x2<x3, the definition given in the wikipedia page gives Q(1)=x3, for 2/3<=p<1, Q(p)=x2, for 1/3<=p<2/3, Q(p)=x1, for 0<=p<1/3, Q(p)=-\infty.
 * With Larry's definition, we get for the same example Q(1)=infty, for 2/3<=p<1, Q(p)=x3, for 1/3<=p<2/3, Q(p)=x2, for 0<=p<1/3, Q(p)=x1. I don't see any good reason to use this definition (the one given on the wikipedia page has nice properties eg for random variate generation). Csaba Szepesvari (talk) 03:52, 15 January 2023 (UTC)

= Signum Function Example = To keep consistent notation with the Sign function article, use sgn(x) instead of sign(x). This would also alleviate the need to explain that the reader shouldn't confuse it with the sine function. — Preceding unsigned comment added by 165.130.136.208 (talk) 22:11, 6 May 2014 (UTC)

External links modified
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I have just modified 4 one external links on Quantile function. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive http://web.archive.org/web/20120324042025/http://course.shufe.edu.cn:80/jpkc/jrjlx/ref/StaTable.pdf to http://course.shufe.edu.cn/jpkc/jrjlx/ref/StaTable.pdf
 * Added archive http://web.archive.org/web/20070505093933/http://home.online.no:80/~pjacklam/notes/invnorm/ to http://home.online.no/~pjacklam/notes/invnorm/
 * Added archive http://web.archive.org/web/20070609171237/http://www.mth.kcl.ac.uk/~shaww/web_page/papers/NormalQuantile1.pdf to http://www.mth.kcl.ac.uk/~shaww/web_page/papers/NormalQuantile1.pdf
 * Added archive http://web.archive.org/web/20070508022437/http://www.mth.kcl.ac.uk:80/~shaww/web_page/papers/Tdistribution06.pdf to http://www.mth.kcl.ac.uk/~shaww/web_page/papers/Tdistribution06.pdf

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Definition
"In terms of the distribution function F, the quantile function Q returns the value x such that [...]" (emphasis by me)

In general, the pre-image is not a singleton. Hence, one cannot talk about the value without further constraints. --80.255.97.37 (talk) 07:45, 30 September 2020 (UTC)