doc/source/tutorial/stats/continuous_halfnorm.rst
.. _continuous-halfnorm:
This is a special case of the chi distribution with :math:L=a and :math:S=b and :math:\nu=1. This is also a special case of the folded normal with shape parameter :math:c=0 and :math:S=S. If :math:Z is (standard) normally distributed then, :math:\left|Z\right| is half-normal. The standard form is
.. math:: :nowrap:
\begin{eqnarray*} f\left(x\right) & = & \sqrt{\frac{2}{\pi}}e^{-x^{2}/2}\\
F\left(x\right) & = & 2\Phi\left(x\right)-1\\
G\left(q\right) & = & \Phi^{-1}\left(\frac{1+q}{2}\right)\end{eqnarray*}
.. math::
M\left(t\right)=\sqrt{2\pi}e^{t^{2}/2}\Phi\left(t\right)
.. math:: :nowrap:
\begin{eqnarray*} \mu & = & \sqrt{\frac{2}{\pi}}\\
\mu_{2} & = & 1-\frac{2}{\pi}\\
\gamma_{1} & = & \frac{\sqrt{2}\left(4-\pi\right)}{\left(\pi-2\right)^{3/2}}\\
\gamma_{2} & = & \frac{8\left(\pi-3\right)}{\left(\pi-2\right)^{2}}\\
m_{d} & = & 0\\
m_{n} & = & \Phi^{-1}\left(\frac{3}{4}\right)\end{eqnarray*}
.. math:: :nowrap:
\begin{eqnarray*} h\left[X\right] & = & \log\left(\sqrt{\frac{\pi e}{2}}\right)\\ & \approx & 0.72579135264472743239.\end{eqnarray*}
Implementation: scipy.stats.halfnorm