This is documentation for an old release of SciPy (version 1.6.3). Read this page in the documentation of the latest stable release (version 1.15.1).
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