Type-2 Gumbel distribution
In probability theory, the Type-2 Gumbel probability density function is
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.
Generating random variates
Given a random variate drawn from the uniform distribution in the interval then the variatehas 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 would yield a negative and hence a negative probability density, which is not allowed.
- If is Type-2 Gumbel-distributed with parameters and, then.
Based on used under GFDL.