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.