麦克斯韦分布¶
这是CHI分布的一个特例，具有 \(L=0\) 和 \(S=\frac{{1}}{{\sqrt{{a}}}}\) 和 \(\nu=3.\) 支持是 \(x\geq0\) 。
\BEGIN{eqnarray*}f\Left(x\Right)&=&\sqrt{\frac{2}{\pi}}x^{2}e^{-x^{2}/2}\\
F\Left(x\Right)&=&\frac{\Gamma\Left(\frac{3}{2}，\frac{x^2}{2}\right)}{\Gamma(\frac{3}{2})}\\
g\Left(Q\Right)&=&\sqrt{2\Gamma^{-1}\Left(\frac{3}{2}，Q\Gamma(\frac{3}{2})\Right)}\end{eqnarray*}
\BEGIN{eqnarray*}\mu&=&2\sqrt{\frac{2}{\pi}}\\
\mu{2}&=&3-\frac{8}{\pi}\\
\Gamma_{1}&=&\sqrt{2}\frac{32-10\pi}{\left(3\pi-8\right)^{3/2}}\\
\Gamma_{2}&=&\frac{-12\pi^{2}+160\pi-384}{\left(3\pi-8\right)^{2}}\\
m_{d}&=&\sqrt{2}\\
m_{n}&=&\sqrt{2\Gamma^{-1}\Left(\frac{3}{2}，\frac{1}{2}\Gamma(\frac{3}{2})\right)}\end{eqnarray*}
\[h\left[X\right]=\log\left(\sqrt{\frac{2\pi}{e}}\right)+\gamma.\]