Type-2 Gumbel distribution
|Probability density function|
|Cumulative distribution function|
|Probability density function (pdf)|
|Cumulative distribution function (cdf)|
|Moment-generating function (mgf)|
This implies that it 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.
The moments exist for
The special case b = 1 yelds the Fréchet distribution
Based on gsl-ref_19.html#SEC309, used under GFDL.