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.. _continuous-rice:
Rice Distribution
=================
There is one shape parameter :math:`b\geq0` (the "distance from the origin") and the support is :math:`x\geq0`.
.. math::
:nowrap:
\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 :math:`I_{0}(y)` is the modified Bessel function of the first kind of order 0.
.. math::
\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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