Type-2 Gumbel distribution

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Type-2 Gumbel
Parameters (real)
shape (real)

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.

See also[edit]