# Fréchet distribution

Fréchet distribution

Probability distribution
name =Fréchet
type =density
pdf_

cdf_

parameters =$alpha in \left(0,infty\right]$ shape
support =$x>0$
pdf =$alpha ; x^\left\{-1-alpha\right\} ; e^\left\{-x^\left\{-alpha$

cdf =$e^\left\{-x^\left\{-alpha$
mean =$Gammaleft\left(1-frac\left\{1\right\}\left\{alpha\right\} ight\right) ext\left\{ if \right\} alpha>1$
median =$left\left(frac\left\{1\right\}\left\{log_e\left(2\right)\right\} ight\right)^\left\{1/alpha\right\}$
mode =$left\left(frac\left\{alpha\right\}\left\{1+alpha\right\} ight\right)^\left\{1/alpha\right\}$
variance =$Gammaleft\left(1-frac\left\{2\right\}\left\{alpha\right\} ight\right)- left\left(Gammaleft\left(1-frac\left\{1\right\}\left\{alpha\right\} ight\right) ight\right)^2 ext\left\{ if \right\} alpha>2$
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

ee also

*Type-2 Gumbel distribution

* [http://www.bankofengland.co.uk/publications/workingpapers/wp287.pdf Bank of England working paper]
* [http://www.emeraldinsight.com/Insight/ViewContentServlet?Filename=Published/EmeraldFullTextArticle/Articles/0830160102.html#0830160102006.pngAn application of a new extreme value distribution to air pollution data]
* [http://www.maths.lth.se/matstat/wafo/documentation/wafodoc/wafo/wstats/wfrechstat.html Wave Analysis for Fatigue and Oceanography]
* [http://www.worldscibooks.com/mathematics/etextbook/p191/p191_chap1_1.pdf "EXTREME VALUE DISTRIBUTIONS Theory and Applications", Kotz & Nadarajah]

Publications

* Fréchet, M., (1927). "Sur la loi de probabilité de l'écart maximum." Ann. Soc. Polon. Math. 6, 93.
* Fisher, R.A., Tippett, L.H.C., (1928). "Limiting forms of the frequency distribution of the largest and smallest member of a sample." Proc. Cambridge Philosophical Society 24:180-190.
* Gumbel, E.J. (1958). "Statistics of Extremes." Columbia University Press, New York.

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