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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
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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Related distributions
- The special case yields the Fréchet distribution.
- 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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