# Type-2 Gumbel distribution

In probability theory, the **Type-2 Gumbel probability density function** is

Parameters |
(real) shape (real) | ||
---|---|---|---|

CDF | |||

Mean | |||

Variance |

for

- .

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.

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