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Type-2 Gumbel distribution

Probability distribution From Wikipedia, the free encyclopedia

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In probability theory, the Type-2 Gumbel probability density function is

for
Quick Facts Parameters, Support ...

For the mean is infinite. For the variance is infinite.

The cumulative distribution function is

The moments exist for

The distribution is named after Emil Julius Gumbel (1891 – 1966).

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Generating random variates

Given a random variate drawn from the uniform distribution in the interval then the variate

has a Type-2 Gumbel distribution with parameter and This is obtained by applying the inverse transform sampling-method.

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  • Substituting and yields the Weibull distribution. Note, however, that a positive (as in the Weibull distribution) would yield a negative and hence a negative probability density, which is not allowed.

Based on "Gumbel distribution". The GNU Scientific Library. type 002d2, used under GFDL.

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See also

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