import numpy as np
from pytensor_distributions import halfnormal as ptd_halfnormal
from preliz.distributions.distributions import Continuous
from preliz.internal.distribution_helper import (
all_not_none,
eps,
from_precision,
pytensor_jit,
pytensor_rng_jit,
to_precision,
)
[docs]
class HalfNormal(Continuous):
r"""
HalfNormal Distribution.
The pdf of this distribution is
.. math::
f(x \mid \sigma) =
\sqrt{\frac{2}{\pi\sigma^2}}
\exp\left(\frac{-x^2}{2\sigma^2}\right)
.. plot::
:context: close-figs
from preliz import HalfNormal, style
style.use('preliz-doc')
for sigma in [0.4, 2.]:
HalfNormal(sigma).plot_pdf(support=(0,5))
======== ==========================================
Support :math:`x \in [0, \infty)`
Mean :math:`\dfrac{\sigma \sqrt{2}}{\sqrt{\pi}}`
Variance :math:`\sigma^2\left(1 - \dfrac{2}{\pi}\right)`
======== ==========================================
HalfNormal distribution has 2 alternative parameterizations. In terms of sigma (standard
deviation) or tau (precision).
The link between the 2 alternatives is given by
.. math::
\tau = \frac{1}{\sigma^2}
Parameters
----------
sigma : float
Scale parameter :math:`\sigma` (``sigma`` > 0).
tau : float
Precision :math:`\tau` (``tau`` > 0).
"""
def __init__(self, sigma=None, tau=None):
super().__init__()
self.support = (0, np.inf)
self._parametrization(sigma, tau)
def _parametrization(self, sigma=None, tau=None):
if all_not_none(sigma, tau):
raise ValueError("Incompatible parametrization. Either use sigma or tau.")
self.param_names = ("sigma",)
self.params_support = ((eps, np.inf),)
if tau is not None:
sigma = from_precision(tau)
self.param_names = ("tau",)
self.sigma = sigma
self.tau = tau
if self.sigma is not None:
self._update(self.sigma)
def _update(self, sigma):
self.sigma = np.float64(sigma)
self.tau = to_precision(self.sigma)
if self.param_names[0] == "sigma":
self.params = (self.sigma,)
elif self.param_names[0] == "tau":
self.params = (self.tau,)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.sigma)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.sigma)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.sigma)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.sigma)
[docs]
def entropy(self):
return ptd_entropy(self.sigma)
[docs]
def mean(self):
return ptd_mean(self.sigma)
[docs]
def mode(self):
return ptd_mode(self.sigma)
[docs]
def var(self):
return ptd_var(self.sigma)
[docs]
def std(self):
return ptd_std(self.sigma)
[docs]
def skewness(self):
return ptd_skewness(self.sigma)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.sigma)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.sigma)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.sigma)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.sigma)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.sigma)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.sigma, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
self._update(sigma / (1 - 2 / np.pi) ** 0.5)
def _fit_mle(self, sample):
self._update(np.mean(sample**2) ** 0.5)
@pytensor_jit
def ptd_pdf(x, sigma):
return ptd_halfnormal.pdf(x, sigma)
@pytensor_jit
def ptd_cdf(x, sigma):
return ptd_halfnormal.cdf(x, sigma)
@pytensor_jit
def ptd_ppf(q, sigma):
return ptd_halfnormal.ppf(q, sigma)
@pytensor_jit
def ptd_logpdf(x, sigma):
return ptd_halfnormal.logpdf(x, sigma)
@pytensor_jit
def ptd_entropy(sigma):
return ptd_halfnormal.entropy(sigma)
@pytensor_jit
def ptd_mean(sigma):
return ptd_halfnormal.mean(sigma)
@pytensor_jit
def ptd_mode(sigma):
return ptd_halfnormal.mode(sigma)
@pytensor_jit
def ptd_median(sigma):
return ptd_halfnormal.median(sigma)
@pytensor_jit
def ptd_var(sigma):
return ptd_halfnormal.var(sigma)
@pytensor_jit
def ptd_std(sigma):
return ptd_halfnormal.std(sigma)
@pytensor_jit
def ptd_skewness(sigma):
return ptd_halfnormal.skewness(sigma)
@pytensor_jit
def ptd_kurtosis(sigma):
return ptd_halfnormal.kurtosis(sigma)
@pytensor_jit
def ptd_lmoment1(sigma):
return ptd_halfnormal.lmoment1(sigma)
@pytensor_jit
def ptd_lmoment2(sigma):
return ptd_halfnormal.lmoment2(sigma)
@pytensor_jit
def ptd_lmoment3(sigma):
return ptd_halfnormal.lmoment3(sigma)
@pytensor_jit
def ptd_lmoment4(sigma):
return ptd_halfnormal.lmoment4(sigma)
@pytensor_rng_jit
def ptd_rvs(sigma, size, rng):
return ptd_halfnormal.rvs(sigma, size=size, random_state=rng)
