Definitions

# Fréchet distribution

{{Probability distribution |
name       =Fréchet|
type       =density|
pdf_image  =|
cdf_image  =|
parameters =$alpha in \left(0,infty\right]$ shape|
support    =$x>0$|
pdf =$alpha ; x^\left\{-1-alpha\right\} ; e^\left\{-x^\left\{-alpha\right\}\right\}$| cdf =$e^\left\{-x^\left\{-alpha\right\}\right\}$| mean =$Gammaleft\left(1-frac\left\{1\right\}\left\{alpha\right\}right\right) text\left\{ if \right\} alpha>1$| median =$left\left(frac\left\{1\right\}\left\{log_e\left(2\right)\right\}right\right)^\left\{1/alpha\right\}$| mode =$left\left(frac\left\{alpha\right\}\left\{1+alpha\right\}right\right)^\left\{1/alpha\right\}$| variance =$Gammaleft\left(1-frac\left\{2\right\}\left\{alpha\right\}right\right)- left\left(Gammaleft\left(1-frac\left\{1\right\}\left\{alpha\right\}right\right)right\right)^2text\left\{ if \right\} alpha>2$|
skewness   =|
g_k        =|
kurtosis   =|
entropy    =|
mgf        =|
char       =|
}}

The Fréchet distribution is a special case of the generalized extreme value distribution. It has the cumulative probability function

where α>0 is a shape parameter. It can be generalised to include a location parameter m and a scale parameter s>0 with the cumulative probability function

Named for Maurice Fréchet who wrote a related paper in 1927, further work was done by Fisher and Tippett in 1928 and by Gumbel in 1958