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Gumbel's Distribution

A special case of the Fisher-Tippett Distribution with $a=0$, $b=1$. The Mean, Variance, Skewness, and Kurtosis are

$\displaystyle \mu$ $\textstyle =$ $\displaystyle \gamma$  
$\displaystyle \sigma^2$ $\textstyle =$ $\displaystyle {\textstyle{1\over 6}}\pi^2$  
$\displaystyle \gamma_1$ $\textstyle =$ $\displaystyle {12\sqrt{6}\,\zeta(3)\over\pi^3}$  
$\displaystyle \gamma_2$ $\textstyle =$ $\displaystyle {\textstyle{12\over 5}}.$  

where $\gamma$ is the Euler-Mascheroni Constant, and $\zeta(3)$ is Apéry's Constant.

See also Fisher-Tippett Distribution




© 1996-9 Eric W. Weisstein
1999-05-25