GumbelDistribution

GumbelDistribution[α,β]
represents a Gumbel distribution with location parameter α and scale parameter β.

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

DetailsDetails

  • 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 allows α and β to be any quantities of the same unit dimensions. »
  • GumbelDistribution can be used with such functions as Mean, CDF, and RandomVariate. »

Background & Context
Background & Context

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Probability density function:

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Cumulative distribution function:

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Mean and variance:

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Median:

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Introduced in 2007
(6.0)
| Updated in 2016
(10.4)