Fréchet distribution

Probability distribution
name =Fréchet
type =density
pdf_

cdf_

parameters =$alpha\; in\; (0,infty]$ shape
support =$x>0$
pdf =$alpha\; ;\; x^\{-1-alpha\}\; ;\; e^\{-x^\{-alpha$
cdf =$e^\{-x^\{-alpha$
mean =$Gammaleft(1-frac\{1\}\{alpha\}\; ight)\; ext\{\; if\; \}\; alpha>1$
median =$left(frac\{1\}\{log\_e(2)\}\; ight)^\{1/alpha\}$
mode =$left(frac\{alpha\}\{1+alpha\}\; ight)^\{1/alpha\}$
variance =$Gammaleft(1-frac\{2\}\{alpha\}\; ight)-\; left(Gammaleft(1-frac\{1\}\{alpha\}\; ight)\; ight)^2\; ext\{\; if\; \}\; alpha>2$
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

External links

* [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.