Talk:Gumbel distribution

This article is a mess, and needs rewriting. -- Anon.


 * I agree; maybe I'll get to it at some point. I've done some small fixes, but more is needed. Michael Hardy 22:11, 23 Feb 2004 (UTC)

If I may give a suggestion, I would redirect the page to the on the generalized extreme value distribution (which I just wrote and I hope in a decent way) of which the Fisher-Tippett is a special case. Since I'm a newbie, I'm not sure it is appropriate to do so, so I prefer to ask.

At any rate, the total lack of any references is troubling, and the fact that neither Pi nor the Euler constant are expressly defined is sloppy. -- Anon.

Gumbel distribution itself makes readers be confused because there are several different definitions of Gumbel distributions. The Gumbel distribution in Wikipedia is the Generalized Extreme Value distribution Type-I. However, other sources such as Wolfram does not follow this definition and they refer Gumbel distribution as a minimum extreme value distribution. In addition, you can see other definitions of Gumbel distribution in several textbooks. For this reason, Matlab does not use the term Gumbel distribution and they don't have any function that directly refers Gumbel distribution. Instead of using the term Gumbel, Mathworks uses "Generalized Extreme Value" distribution (e.g. gevrnd). I agree their way to avoid directly using the term Gumbel distribution in their software because there are many different definitions of Gumbel distributions. Wikipedia editors also have to carefully edit this page. -- Jaekwan — Preceding unsigned comment added by Jkshin933 (talk • contribs) 21:07, 3 October 2016 (UTC)

Symbol mismatch - text and graphics
The images use symbols β and γ, but the text uses β and μ. One or the other needs correcting for consistency. DFH 20:25, 30 January 2007 (UTC)


 * I suppose those symbols are BETA, GAMMA, and MU. In the table at right MU is the location parameter which is not the mean.
 * The two top right graphs use parameters LAMBDA and BETA but the table below them uses MU and BETA. Is LAMBDA also the location parameter?
 * Is consistency across articles on probability distributions intended regarding symbols for location, scale, and shape parameters? If not entirely, is consistency intended for the top right graphs?  for the righthand tables?  —Preceding unsigned comment added by 140.247.23.33 (talk) 23:56, 14 November 2007 (UTC)

changed the figures to remove the figure inconsistencies. --Herr blaschke (talk) 11:12, 26 March 2008 (UTC)

Distribution name
Isn't this also called the Gompertz distribution? If you see, the Shifted Gompertz distribution links this distribution, but nothing is written here about the other name, so it is confusing. Faermi 16:03, 16 May 2007 (UTC)

Mean Value Calculation
I think that tere is a mistake in the calculation of the mean value, because I've done some experiments in Mattab and the sign in the equation should be (-), i.e., mean$$=\mu - \beta\,\gamma\!$$, and not mean$$=\mu + \beta\,\gamma\!$$, as it was before.

Anyone can confirm if that's right?

Thank you all.

08:37, 3 April 2008 (UTC)

Response: see Location-scale_family for the rules of location scale transormations. Also, it is cited with a + in the body of the article. If you are careful with the - signs in the distribution, you will see that the + sign in the mean is the correct formula. —Preceding unsigned comment added by 131.110.112.62 (talk) 20:17, 4 April 2008 (UTC)

Response 2: Matlab has a different definition of the Gumbel distribution from that used here (it has a heavy left tail). Thus the mean of the Matlab Gumbel distribution is indeed $$=\mu - \beta\,\gamma\!$$. This caused someone to incorrectly change the sign to minus on 27 Nov. 2010. I have now changed it back to plus. Kristjan.Jonasson (talk) 11:55, 30 December 2010 (UTC)

Gumbel graph paper
The attached image of the graph paper doesn't make much sense. How is it related to this distribution? This should be explained. --Ghtx (talk) 15:27, 5 May 2009 (UTC)

i think something is wrong. the maximum is not the first order statistic? which ( the first order statistic or the nth order statistic) is distributed as gumbel? —Preceding unsigned comment added by 41.91.62.24 (talk) 15:06, 25 November 2010 (UTC)

Minimum vs Maximum Case
From the text: "It is also known as the log-Weibull distribution"

Actually, per NIST, the Gumbel (minimum case) distribution is the distribution of the log of a Weibull-distributed variable, whereas this page is talking about the Gumbel (maximum case) distribution... — Preceding unsigned comment added by 2001:4898:0:FFF:0:5EFE:A7D:8603 (talk) 21:32, 26 October 2012 (UTC)

Sum of two Gumble variables
The formula under Related distributions, claiming that for Gumble X and Y, X+Y is Logistic seems incorrect. Simple argument: X+Y should not be symmetric.

More complicated argument: Saralees Nadarajah "Linear combination of Gumbel random variables" (2006) Gives expression for the cdf of the sum (Corollary 2), and it is a Bassel function.

The same applies also to the similar formula for generalized extreme value distribution. — Preceding unsigned comment added by Alexander Shekhovtsov (CTU) (talk • contribs) 16:19, 9 July 2018 (UTC)