CHI分布¶
通过取卡方变量的(正)平方根生成的。一个形状参数是 \(\nu\) ，正整数，自由度。支持是 \(x\geq0\) 。
\Begin{eqnarray*}f\Left(x；\nu\Right)&=&\frac{x^{\nu-1}e^{-x^{2}/2}}{2^{\nu/2-1}\Gamma\left(\frac{\nu}{2}\right)}\\
F\Left(x；\nu\Right)&=&\frac{\Gamma\Left(\frac{\nu}{2}，\frac{x^{2}}{2}\right)}{\Gamma(\frac{\nu}{2})}\\
g\Left(q；\nu\Right)&=&\sqrt{2\Gamma^{-1}\Left(\frac{\nu}{2}，q\Gamma(\frac{\nu}{2})\Right)}\\
M\Left(t\Right)&=&\Gamma\Left(\frac{v}{2}\right)\，_{1}F_{1}\Left(\frac{v}{2}；\frac{1}{2}；\frac{t^{2}}{2}\right)+\frac{t}{\sqrt{2}}\Gamma\left(\frac{1+\nu}{2}\right)\，_{1}F_{1}\left(\frac{1+\nu}{2}；\frac{3}{2}；\frac{t^{2}}{2}\right)\\
\MU&=&\frac{\sqrt{2}\Gamma\left(\frac{\nu+1}{2}\right)}{\Gamma\left(\frac{\nu}{2}\right)}\\
\MU_{2}&=&\nu-\MU^{2}\\
\Gamma_{1}&=&\frac{2\mu^{3}+\mu\left(1-2\nu\right)}{\mu_{2}^{3/2}}\\
\Gamma_{2}&=&\frac{2\nu\left(1-\nu\right)-6\mu^{4}+4\mu^{2}\left(2\nu-1\right)}{\mu_{2}^{2}}\\
m_{d}&=&\sqrt{\nu-1}\quad\nu\geq1\\
m_{n}&=&\sqrt{2\Gamma^{-1}\Left(\frac{\nu}{2}，\frac{1}{2}{\Gamma(\frac{\nu}{2})}\right)}\end{eqnarray*}
实施： scipy.stats.chi