# Rice Distribution¶

There is one shape parameter $$b\geq0$$ (the “distance from the origin”) and the support is $$x\geq0$$.

\begin{eqnarray*} f\left(x;b\right) & = & x\exp\left(-\frac{x^{2}+b^{2}}{2}\right)I_{0}\left(xb\right)\\ F\left(x;b\right) & = & \int_{0}^{x}\alpha\exp\left(-\frac{\alpha^{2}+b^{2}}{2}\right)I_{0}\left(\alpha b\right)d\alpha\end{eqnarray*}

were $$I_{0}(y)$$ is the modified Bessel function of the first kind of order 0.

$\mu_{n}^{\prime}=\sqrt{2^{n}}\Gamma\left(1+\frac{n}{2}\right)\,_{1}F_{1}\left(-\frac{n}{2};1;-\frac{b^{2}}{2}\right)$

Implementation: scipy.stats.rice

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