import numpy as np
from pytensor_distributions import rice as ptd_rice
from preliz.distributions.distributions import Continuous
from preliz.internal.distribution_helper import all_not_none, eps, pytensor_jit, pytensor_rng_jit
from preliz.internal.optimization import optimize_ml, optimize_moments_rice
[docs]
class Rice(Continuous):
r"""
Rice distribution.
The pdf of this distribution is
.. math::
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)
.. plot::
:context: close-figs
from preliz import Rice, style
style.use('preliz-doc')
nus = [0., 0., 4.]
sigmas = [1., 2., 2.]
for nu, sigma in zip(nus, sigmas):
Rice(nu, sigma).plot_pdf(support=(0,10))
======== ==============================================================
Support :math:`x \in (0, \infty)`
Mean :math:`\sigma \sqrt{\pi /2} L_{1/2}(-\nu^2 / 2\sigma^2)`
Variance :math:`2\sigma^2 + \nu^2 - \frac{\pi \sigma^2}{2}`
:math:`L_{1/2}^2\left(\frac{-\nu^2}{2\sigma^2}\right)`
======== ==============================================================
Rice distribution has 2 alternative parameterizations. In terms of nu and sigma
or b and sigma.
The link between the two parametrizations is given by
.. math::
b = \dfrac{\nu}{\sigma}
Parameters
----------
nu : float
Noncentrality parameter.
sigma : float
Scale parameter.
b : float
Shape parameter.
"""
def __init__(self, nu=None, sigma=None, b=None):
super().__init__()
self.name = "rice"
self.support = (0, np.inf)
self._parametrization(nu, sigma, b)
def _parametrization(self, nu=None, sigma=None, b=None):
if all_not_none(nu, b):
raise ValueError(
"Incompatible parametrization. Either use nu and sigma or b and sigma."
)
self.param_names = ("nu", "sigma")
self.params_support = ((eps, np.inf), (eps, np.inf))
if b is not None:
self.b = b
self.sigma = sigma
self.param_names = ("b", "sigma")
if all_not_none(b, sigma):
nu = self._from_b(b, sigma)
self.nu = nu
self.sigma = sigma
if all_not_none(self.nu, self.sigma):
self._update(self.nu, self.sigma)
def _from_b(self, b, sigma):
nu = b * sigma
return nu
def _to_b(self, nu, sigma):
b = nu / sigma
return b
def _update(self, nu, sigma):
self.nu = np.float64(nu)
self.sigma = np.float64(sigma)
self.b = self._to_b(self.nu, self.sigma)
if self.param_names[0] == "nu":
self.params = (self.nu, self.sigma)
elif self.param_names[0] == "b":
self.params = (self.b, self.sigma)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.nu, self.sigma)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.nu, self.sigma)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.nu, self.sigma)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.nu, self.sigma)
[docs]
def entropy(self):
return ptd_entropy(self.nu, self.sigma)
[docs]
def mean(self):
return ptd_mean(self.nu, self.sigma)
[docs]
def var(self):
return ptd_var(self.nu, self.sigma)
[docs]
def std(self):
return ptd_std(self.nu, self.sigma)
[docs]
def skewness(self):
return ptd_skewness(self.nu, self.sigma)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.nu, self.sigma)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.nu, self.sigma)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.nu, self.sigma)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.nu, self.sigma)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.nu, self.sigma)
[docs]
def rvs(self, size=1, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.nu, self.sigma, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
nu, sigma = optimize_moments_rice(mean, sigma)
self._update(nu, sigma)
def _fit_mle(self, sample):
optimize_ml(self, sample)
@pytensor_jit
def ptd_pdf(x, nu, sigma):
return ptd_rice.pdf(x, nu, sigma)
@pytensor_jit
def ptd_cdf(x, nu, sigma):
return ptd_rice.cdf(x, nu, sigma)
@pytensor_jit
def ptd_ppf(q, nu, sigma):
return ptd_rice.ppf(q, nu, sigma)
@pytensor_jit
def ptd_logpdf(x, nu, sigma):
return ptd_rice.logpdf(x, nu, sigma)
@pytensor_jit
def ptd_entropy(nu, sigma):
return ptd_rice.entropy(nu, sigma)
@pytensor_jit
def ptd_mean(nu, sigma):
return ptd_rice.mean(nu, sigma)
@pytensor_jit
def ptd_mode(nu, sigma):
return ptd_rice.mode(nu, sigma)
@pytensor_jit
def ptd_median(nu, sigma):
return ptd_rice.median(nu, sigma)
@pytensor_jit
def ptd_var(nu, sigma):
return ptd_rice.var(nu, sigma)
@pytensor_jit
def ptd_std(nu, sigma):
return ptd_rice.std(nu, sigma)
@pytensor_jit
def ptd_skewness(nu, sigma):
return ptd_rice.skewness(nu, sigma)
@pytensor_jit
def ptd_kurtosis(nu, sigma):
return ptd_rice.kurtosis(nu, sigma)
@pytensor_jit
def ptd_lmoment1(nu, sigma):
return ptd_rice.lmoment1(nu, sigma)
@pytensor_jit
def ptd_lmoment2(nu, sigma):
return ptd_rice.lmoment2(nu, sigma)
@pytensor_jit
def ptd_lmoment3(nu, sigma):
return ptd_rice.lmoment3(nu, sigma)
@pytensor_jit
def ptd_lmoment4(nu, sigma):
return ptd_rice.lmoment4(nu, sigma)
@pytensor_rng_jit
def ptd_rvs(nu, sigma, size, rng):
return ptd_rice.rvs(nu, sigma, size=size, random_state=rng)
