Type-2 Gumbel distribution

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).

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.

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.

• If is Type-2 Gumbel-distributed with parameters and , then .

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Based on used under GFDL.

See also

• Extreme value theory
• Gumbel distribution