import numpy as np
from pytensor_distributions import cauchy as ptd_cauchy
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
[docs]
class Cauchy(Continuous):
r"""
Cauchy Distribution.
The pdf of this distribution is
.. math::
f(x \mid \alpha, \beta) =
\frac{1}{\pi \beta [1 + (\frac{x-\alpha}{\beta})^2]}
.. plot::
:context: close-figs
from preliz import Cauchy, style
style.use('preliz-doc')
alphas = [0., 0., -2.]
betas = [.5, 1., 1.]
for alpha, beta in zip(alphas, betas):
Cauchy(alpha, beta).plot_pdf(support=(-5,5))
======== ==============================================================
Support :math:`x \in \mathbb{R}`
Mean undefined
Variance undefined
======== ==============================================================
Parameters
----------
alpha : float
Location parameter.
beta : float
Scale parameter > 0.
"""
def __init__(self, alpha=None, beta=None):
super().__init__()
self.support = (-np.inf, np.inf)
self._parametrization(alpha, beta)
def _parametrization(self, alpha=None, beta=None):
self.alpha = alpha
self.beta = beta
self.param_names = ("alpha", "beta")
self.params_support = ((-np.inf, np.inf), (eps, np.inf))
self.params = (self.alpha, self.beta)
if all_not_none(alpha, beta):
self._update(alpha, beta)
def _update(self, alpha, beta):
self.alpha = np.float64(alpha)
self.beta = np.float64(beta)
self.params = (self.alpha, self.beta)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.alpha, self.beta)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.alpha, self.beta)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.alpha, self.beta)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.alpha, self.beta)
[docs]
def entropy(self):
return ptd_entropy(self.alpha, self.beta)
[docs]
def mean(self):
return ptd_mean(self.alpha, self.beta)
[docs]
def mode(self):
return ptd_mode(self.alpha, self.beta)
[docs]
def var(self):
return ptd_var(self.alpha, self.beta)
[docs]
def std(self):
return ptd_std(self.alpha, self.beta)
[docs]
def skewness(self):
return ptd_skewness(self.alpha, self.beta)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.alpha, self.beta)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.alpha, self.beta)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.alpha, self.beta)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.alpha, self.beta)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.alpha, self.beta)
[docs]
def logcdf(self, x):
return ptd_logcdf(x, self.alpha, self.beta)
[docs]
def logsf(self, x):
return ptd_logsf(x, self.alpha, self.beta)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.alpha, self.beta, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
self._update(mean, sigma)
def _fit_mle(self, sample):
optimize_ml(self, sample)
@pytensor_jit
def ptd_pdf(x, alpha, beta):
return ptd_cauchy.pdf(x, alpha, beta)
@pytensor_jit
def ptd_cdf(x, alpha, beta):
return ptd_cauchy.cdf(x, alpha, beta)
@pytensor_jit
def ptd_ppf(q, alpha, beta):
return ptd_cauchy.ppf(q, alpha, beta)
@pytensor_jit
def ptd_logpdf(x, alpha, beta):
return ptd_cauchy.logpdf(x, alpha, beta)
@pytensor_jit
def ptd_entropy(alpha, beta):
return ptd_cauchy.entropy(alpha, beta)
@pytensor_jit
def ptd_mean(alpha, beta):
return ptd_cauchy.mean(alpha, beta)
@pytensor_jit
def ptd_mode(alpha, beta):
return ptd_cauchy.mode(alpha, beta)
@pytensor_jit
def ptd_median(alpha, beta):
return ptd_cauchy.median(alpha, beta)
@pytensor_jit
def ptd_var(alpha, beta):
return ptd_cauchy.var(alpha, beta)
@pytensor_jit
def ptd_std(alpha, beta):
return ptd_cauchy.std(alpha, beta)
@pytensor_jit
def ptd_skewness(alpha, beta):
return ptd_cauchy.skewness(alpha, beta)
@pytensor_jit
def ptd_kurtosis(alpha, beta):
return ptd_cauchy.kurtosis(alpha, beta)
@pytensor_jit
def ptd_lmoment1(alpha, beta):
return ptd_cauchy.lmoment1(alpha, beta)
@pytensor_jit
def ptd_lmoment2(alpha, beta):
return ptd_cauchy.lmoment2(alpha, beta)
@pytensor_jit
def ptd_lmoment3(alpha, beta):
return ptd_cauchy.lmoment3(alpha, beta)
@pytensor_jit
def ptd_lmoment4(alpha, beta):
return ptd_cauchy.lmoment4(alpha, beta)
@pytensor_jit
def ptd_logcdf(x, alpha, beta):
return ptd_cauchy.logcdf(x, alpha, beta)
@pytensor_jit
def ptd_logsf(x, alpha, beta):
return ptd_cauchy.logsf(x, alpha, beta)
@pytensor_rng_jit
def ptd_rvs(alpha, beta, size, rng):
return ptd_cauchy.rvs(alpha, beta, size=size, random_state=rng)
