This is documentation for an old release of SciPy (version 0.15.1). Read this page in the documentation of the latest stable release (version 1.15.1).
Rayleigh Distribution¶
This is Chi distribution with \(L=0.0\) and \(\nu=2\) and \(S=S\) (no location parameter is generally used), the mode of the distribution is \(S.\)
\[ \begin{eqnarray*} f\left(r\right) & = & re^{-r^{2}/2}I_{[0,\infty)}\left(x\right)\\ F\left(r\right) & = & 1-e^{-r^{2}/2}I_{[0,\infty)}\left(x\right)\\ G\left(q\right) & = & \sqrt{-2\log\left(1-q\right)}\end{eqnarray*}\]
\[ \begin{eqnarray*} \mu & = & \sqrt{\frac{\pi}{2}}\\ \mu_{2} & = & \frac{4-\pi}{2}\\ \gamma_{1} & = & \frac{2\left(\pi-3\right)\sqrt{\pi}}{\left(4-\pi\right)^{3/2}}\\ \gamma_{2} & = & \frac{24\pi-6\pi^{2}-16}{\left(4-\pi\right)^{2}}\\ m_{d} & = & 1\\ m_{n} & = & \sqrt{2\log\left(2\right)}\end{eqnarray*}\]
\[h\left[X\right]=\frac{\gamma}{2}+\log\left(\frac{e}{\sqrt{2}}\right).\]
\[\mu_{n}^{\prime}=\sqrt{2^{n}}\Gamma\left(\frac{n}{2}+1\right)\]
Implementation: scipy.stats.rayleigh