半圆形分布¶

定义于 \(x\in\left[-1,1\right]\)

\BEGIN{eqnarray [}} f\left(x\right) & = & \frac{{2}}{{\pi}}\sqrt{{1-x^{{2}}}}\\ F\left(x\right) & = & \frac{{1}}{{2}}+\frac{{1}}{{\pi}}\left[x\sqrt{{1-x^{{2}}}}+\arcsin x\right]\\ G\left(q\right) & = & F^{{-1}}\left(q\right)\end{{eqnarray] }

\BEGIN{eqnarray *}} m_{{d}}=m_{{n}}=\mu & = & 0\\ \mu_{{2}} & = & \frac{{1}}{{4}}\\ \gamma_{{1}} & = & 0\\ \gamma_{{2}} & = & -1\end{{eqnarray* }