The Fréchet distribution, also known as inverse Weibull distribution,[2][3] is a special case of the generalized extreme value distribution.

It has the cumulative distribution function where   α > 0   is a shape parameter.

It can be generalised to include a location parameter m (the minimum) and a scale parameter   s > 0   with the cumulative distribution function Named for Maurice Fréchet who wrote a related paper in 1927,[4] further work was done by Fisher and Tippett in 1928 and by Gumbel in 1958.

[5][6] The single parameter Fréchet, with parameter

has standardized moment (with

is the Gamma function.

can be expressed through the inverse of the distribution, In particular the median is: The mode of the distribution is

Especially for the 3-parameter Fréchet, the first quartile is

log ⁡ ( 4 )

Also the quantiles for the mean and mode are: However, in most hydrological applications, the distribution fitting is via the generalized extreme value distribution as this avoids imposing the assumption that the distribution does not have a lower bound (as required by the Frechet distribution).

[citation needed]