In probability theory, the Type-2 Gumbel probability density function is
This implies that it is similar to the Weibull distributions, substituting and . Note, however, that a positive k (as in the Weibull distribution) would yield a negative a, which is not allowed here as it would yield a negative probability density.
For the mean is infinite. For the variance is infinite.
The cumulative distribution function is
The moments exist for
The special case b = 1 yields the Fréchet distribution.
Based on The GNU Scientific Library, used under GFDL.