represents a Gumbel distribution with location parameter α and scale parameter β.

represents a Gumbel distribution with location parameter 0 and scale parameter 1.


  • The Gumbel distribution gives the asymptotic distribution of the minimum value in a sample from a distribution such as the normal distribution.
  • The asymptotic distribution of the maximum value, also sometimes called a Gumbel distribution, is implemented in the Wolfram Language as ExtremeValueDistribution. »
  • The probability density for value in a Gumbel distribution is proportional to . »
  • GumbelDistribution allows α to be any real number and β to be any positive real number.
  • GumbelDistribution can be used with such functions as Mean, CDF, and RandomVariate. »

Background & Context
Background & Context

Introduced in 2007
| Updated in 2015
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