{{Probability distribution |

 name       =Fréchet|

 type       =density|

 pdf_image  =|

 cdf_image  =|

 parameters =$alpha\; in\; (0,infty]$ shape|

 support    =$x>0$|

pdf =$alpha\; ;\; x^\{-1-alpha\}\; ;\; e^\{-x^\{-alpha\}\}$| cdf =$e^\{-x^\{-alpha\}\}$| mean =$Gammaleft(1-frac\{1\}\{alpha\}right)\; text\{\; if\; \}\; alpha>1$| median =$left(frac\{1\}\{log\_e(2)\}right)^\{1/alpha\}$| mode =$left(frac\{alpha\}\{1+alpha\}right)^\{1/alpha\}$| variance =$Gammaleft(1-frac\{2\}\{alpha\}right)-\; left(Gammaleft(1-frac\{1\}\{alpha\}right)right)^2text\{\; if\; \}\; alpha>2$|

 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

See also

• Type-2 Gumbel distribution

External links

• Bank of England working paper
• An application of a new extreme value distribution to air pollution data
• Wave Analysis for Fatigue and Oceanography
• 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.