Gumbel(LogWeibull，Fisher-Tippetts，I型极值)分布¶
一类极值分布(右偏)之一。
\BEGIN{eqnarray *}} f\left(x\right) & = & \exp\left(-\left(x+e^{{-x}}\right)\right)\\ F\left(x\right) & = & \exp\left(-e^{{-x}}\right)\\ G\left(q\right) & = & -\log\left(-\log\left(q\right)\right)\end{{eqnarray* }
\[M\Left(t\Right)=\Gamma\Left(1-t\Right)\]
\BEGIN{eqnarray *}} \mu & = & \gamma=-\psi_{{0}}\left(1\right)\\ \mu_{{2}} & = & \frac{{\pi^{{2}}}}{{6}}\\ \gamma_{{1}} & = & \frac{{12\sqrt{{6}}}}{{\pi^{{3}}}}\zeta\left(3\right)\\ \gamma_{{2}} & = & \frac{{12}}{{5}}\\ m_{{d}} & = & 0\\ m_{{n}} & = & -\log\left(\log2\right)\end{{eqnarray* }
\[h\left[X\right]\approx1.0608407169541684911\]