Fisher-Tippett Distribution
Also called the Extreme Value Distribution and Log-Weibull Distribution. It is the limiting distributionfor the smallest or largest values in a large sample drawn from a variety of distributions.
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These can be computed directly be defining
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Then the Moments are
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where
are Euler-Mascheroni Integrals. Plugging in the Euler-Mascheroni Integrals gives | |  | (7) |
 | |  | (8) |
 | |  | (9) |
 | |  | (10) |
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 |  | (11) |
where
is the Euler-Mascheroni Constant and 
is Apéry's Constant.The Mean, Variance, Skewness, and Kurtosis are therefore | | | (12) |
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The Characteristic Function is
 | (16) |
is the Gamma Function. The special case of the Fisher-Tippett distribution with 
, 
is calledGumbel's Distribution.See also Euler-Mascheroni Integrals, Gumbel's Distribution- Linear Approximation
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