Source code for preliz.distributions.chi_squared
import numpy as np
from pytensor_distributions import chisquared as ptd_chisquared
from preliz.distributions.distributions import Continuous
from preliz.internal.distribution_helper import eps, pytensor_jit, pytensor_rng_jit
from preliz.internal.optimization import optimize_ml
[docs]
class ChiSquared(Continuous):
r"""
Chi squared distribution.
The pdf of this distribution is
.. math::
f(x \mid \nu) =
\frac{x^{(\nu-2)/2}e^{-x/2}}{2^{\nu/2}\Gamma(\nu/2)}
.. plot::
:context: close-figs
from preliz import ChiSquared, style
style.use('preliz-doc')
nus = [1., 3., 9.]
for nu in nus:
ax = ChiSquared(nu).plot_pdf(support=(0,20))
ax.set_ylim(0, 0.6)
======== ===============================
Support :math:`x \in [0, \infty)`
Mean :math:`\nu`
Variance :math:`2 \nu`
======== ===============================
Parameters
----------
nu : float
Degrees of freedom (nu > 0).
"""
def __init__(self, nu=None):
super().__init__()
self.nu = nu
self.support = (0, np.inf)
self._parametrization(nu)
def _parametrization(self, nu=None):
self.nu = nu
self.param_names = ("nu",)
self.params_support = ((eps, np.inf),)
self.params = (self.nu,)
if self.nu is not None:
self._update(self.nu)
def _update(self, nu):
self.nu = np.float64(nu)
self.params = (self.nu,)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.nu)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.nu)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.nu)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.nu)
[docs]
def entropy(self):
return ptd_entropy(self.nu)
[docs]
def mean(self):
return ptd_mean(self.nu)
[docs]
def mode(self):
return ptd_mode(self.nu)
[docs]
def var(self):
return ptd_var(self.nu)
[docs]
def std(self):
return ptd_std(self.nu)
[docs]
def skewness(self):
return ptd_skewness(self.nu)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.nu)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.nu)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.nu)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.nu)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.nu)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.nu, size=size, rng=random_state)
def _fit_moments(self, mean, sigma=None):
self._update(mean)
def _fit_mle(self, sample):
optimize_ml(self, sample)
@pytensor_jit
def ptd_pdf(x, nu):
return ptd_chisquared.pdf(x, nu)
@pytensor_jit
def ptd_cdf(x, nu):
return ptd_chisquared.cdf(x, nu)
@pytensor_jit
def ptd_ppf(q, nu):
return ptd_chisquared.ppf(q, nu)
@pytensor_jit
def ptd_logpdf(x, nu):
return ptd_chisquared.logpdf(x, nu)
@pytensor_jit
def ptd_entropy(nu):
return ptd_chisquared.entropy(nu)
@pytensor_jit
def ptd_mean(nu):
return ptd_chisquared.mean(nu)
@pytensor_jit
def ptd_mode(nu):
return ptd_chisquared.mode(nu)
@pytensor_jit
def ptd_median(nu):
return ptd_chisquared.median(nu)
@pytensor_jit
def ptd_var(nu):
return ptd_chisquared.var(nu)
@pytensor_jit
def ptd_std(nu):
return ptd_chisquared.std(nu)
@pytensor_jit
def ptd_skewness(nu):
return ptd_chisquared.skewness(nu)
@pytensor_jit
def ptd_kurtosis(nu):
return ptd_chisquared.kurtosis(nu)
@pytensor_jit
def ptd_lmoment1(nu):
return ptd_chisquared.lmoment1(nu)
@pytensor_jit
def ptd_lmoment2(nu):
return ptd_chisquared.lmoment2(nu)
@pytensor_jit
def ptd_lmoment3(nu):
return ptd_chisquared.lmoment3(nu)
@pytensor_jit
def ptd_lmoment4(nu):
return ptd_chisquared.lmoment4(nu)
@pytensor_rng_jit
def ptd_rvs(nu, size, rng):
return ptd_chisquared.rvs(nu, size=size, random_state=rng)
