Gumbel's Distribution

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

$$\mu = \gamma$$

$$\sigma^2 = {\textstyle{1\over 6}}\pi^2$$

$$\gamma_1 = {12\sqrt{6}\,\zeta(3)\over\pi^3}$$

$$\gamma_2 = {\textstyle{12\over 5}}.$$

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

See also Fisher-Tippett Distribution