Fréchet distribution

{{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

External links


  • 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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