Rayleigh Distribution#

This is a special case of the Chi distribution with $L=0.0$ and $\nu=2$ (no location parameter is generally used), the mode of the distribution is $S.$

\begin{array}{rcl} f (r) & = & r e^{- r^{2} / 2} \\ F (r) & = & 1 - e^{- r^{2} / 2} \\ G (q) & = & \sqrt{- 2 \log (1 - q)} \end{array}

$\begin{eqnarray*} f\left(r\right) & = & re^{-r^{2}/2}\\ F\left(r\right) & = & 1-e^{-r^{2}/2}\\ G\left(q\right) & = & \sqrt{-2\log\left(1-q\right)}\end{eqnarray*}$

\begin{array}{rcl} μ & = & \sqrt{\frac{π}{2}} \\ μ_{2} & = & \frac{4 - π}{2} \\ γ_{1} & = & \frac{2 (π - 3) \sqrt{π}}{{(4 - π)}^{3 / 2}} \\ γ_{2} & = & \frac{24 π - 6 π^{2} - 16}{{(4 - π)}^{2}} \\ m_{d} & = & 1 \\ m_{n} & = & \sqrt{2 \log (2)} \end{array}

$\begin{eqnarray*} \mu & = & \sqrt{\frac{\pi}{2}}\\ \mu_{2} & = & \frac{4-\pi}{2}\\ \gamma_{1} & = & \frac{2\left(\pi-3\right)\sqrt{\pi}}{\left(4-\pi\right)^{3/2}}\\ \gamma_{2} & = & \frac{24\pi-6\pi^{2}-16}{\left(4-\pi\right)^{2}}\\ m_{d} & = & 1\\ m_{n} & = & \sqrt{2\log\left(2\right)}\end{eqnarray*}$

h [X] = \frac{γ}{2} + \log (\frac{e}{\sqrt{2}}) .

$h\left[X\right]=\frac{\gamma}{2}+\log\left(\frac{e}{\sqrt{2}}\right).$

μ_{n}^{'} = \sqrt{2^{n}} Γ (\frac{n}{2} + 1)

$\mu_{n}^{\prime}=\sqrt{2^{n}}\Gamma\left(\frac{n}{2}+1\right)$

Implementation: scipy.stats.rayleigh