余弦分布¶
近似于正态分布。支持是 \(\left[-\pi,\pi\right]\) 。
\BEGIN{eqnarray*}f\Left(x\right)&=&\frac{1}{2\pi}\Left(1+\cos x\right)\\
F\Left(x\Right)&=&\frac{1}{2\pi}\Left(\pi+x+\sin x\right)\\
G\Left(Q\Right)&=&F^{-1}\Left(Q\Right)\\
m\Left(t\Right)&=&\frac{\sinh\Left(\pi t\right)}{\pi t\Left(1+t^{2}\right)}\\
\mU=m_{d}=m_{n}&=&0\\
\mU_{2}&=&\frac{\pi^{2}}{3}-2\\
\Gamma_{1}&=&0\\
\Gamma_{2}&=&\frac{-6\left(\pi^{4}-90\right)}{5\left(\pi^{2}-6\right)^{2}}\end{eqnarray*}
\BEGIN{eqnarray*}h\Left [X\right] &=&\log\Left(4\pi\Right)-1\\
&\约&1.5310242469692907930。\end{eqnarray*}