# pymc.Rice#

class pymc.Rice(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, default_transform=UNSET, **kwargs)[source]#

Rice distribution.

$f(x\mid \nu ,\sigma )= {\frac {x}{\sigma ^{2}}}\exp \left({\frac {-(x^{2}+\nu ^{2})}{2\sigma ^{2}}}\right)I_{0}\left({\frac {x\nu }{\sigma ^{2}}}\right),$
 Support $$x \in (0, \infty)$$ Mean $$\sigma {\sqrt {\pi /2}}\,\,L_{{1/2}}(-\nu ^{2}/2\sigma ^{2})$$ Variance $$2\sigma ^{2}+\nu ^{2}-{\frac {\pi \sigma ^{2}}{2}}L_{{1/2}}^{2}\left({\frac {-\nu ^{2}}{2\sigma ^{2}}}\right)$$
Parameters:
nutensor_like of float, optional

Noncentrality parameter (only required if b is not specified).

sigmatensor_like of float, default 1

scale parameter.

btensor_like of float, optional

Shape parameter (alternative to nu, only required if nu is not specified).

Notes

The distribution $$\mathrm{Rice}\left(|\nu|,\sigma\right)$$ is the distribution of $$R=\sqrt{X^2+Y^2}$$ where $$X\sim N(\nu \cos{\theta}, \sigma^2)$$, $$Y\sim N(\nu \sin{\theta}, \sigma^2)$$ are independent and for any real $$\theta$$.

The distribution is defined with either nu or b. The link between the two parametrizations is given by

$b = \dfrac{\nu}{\sigma}$

Methods

 Rice.dist([nu, sigma, b]) Creates a tensor variable corresponding to the cls distribution.