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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.

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