Also called the Extreme Value Distribution and Log-Weibull Distribution. It is the limiting distribution
for the smallest or largest values in a large sample drawn from a variety of distributions.
These can be computed directly be defining
Then the Moments are
where are Euler-Mascheroni Integrals. Plugging in the Euler-Mascheroni Integrals gives
where is the Euler-Mascheroni Constant and is Apéry's Constant.
The Mean, Variance, Skewness, and Kurtosis are therefore
The Characteristic Function is
where is the Gamma Function. The special case of the Fisher-Tippett distribution with , is called
See also Euler-Mascheroni Integrals, Gumbel's Distribution
© 1996-9 Eric W. Weisstein