Fréchet distribution


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:Pr(X ext{ if } x>0. 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 :Pr(X ext{ if } x>m.

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.


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