Fréchet distribution

The Fréchet distribution, also known as inverse Weibull distribution, is a special case of the generalized extreme value distribution. It has the cumulative distribution function The Fréchet distribution, also known as inverse Weibull distribution, is a special case of the generalized extreme value distribution. It has the cumulative distribution function where α > 0 is a shape parameter. It can be generalised to include a location parameter m (the minimum) and a scale parameter s > 0 with the cumulative distribution 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. The single parameter Fréchet with parameter α {displaystyle alpha } has standardized moment (with t = x − α {displaystyle t=x^{-alpha }} ) defined only for k < α {displaystyle k<alpha } : where Γ ( z ) {displaystyle Gamma left(z ight)} is the Gamma function.