Misplaced Pages

This is an old revision of this page, as edited by Karada (talk | contribs) at 23:29, 27 December 2003 (The Gumbel distribution, and similar distributions, are used in extreme value theory.). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

In probability theory and statistics the Gumbel distribution is used to find the minimum (or the maximum) of a number of samples of various distributions. These distributions could be of the normal or exponential type. It is used for the extreme values of water levels, floods and wind velocities. The Gumbel distribution, and similar distributions, are used in extreme value theory.

It is sometimes called the Fisher-Tippett distribution and is defined as

${\displaystyle p=\exp(-\exp((A-x)/B).}$

A more practical way of using the distribution could be

     p=exp(-exp(-0.367*(A-x)/(A-M))  ;-.367=ln(-ln(.5))

where M is the Median.To fit values one could get the Median straight away and then vary A untill it fits the list of values.

Its variates(ie to get a list of random values) can be given as ;

      x=A-B*ln(-ln(rnd))

Its percentiles can be given by ;

      x=A-B*ln(-ln(p))

ie Q1=A-B*ln(-ln(.25))

The Median is A-B*ln(-ln(.5))

 Q3=A-B*ln(-ln(.75))

The mean is A+g*B 'g=Eulers constant = .57721

The sd = B * Pi()* sqr(1/6)

Its mode is A