import numpy as np
import pytensor.tensor as pt
from pytensor_distributions import normal as ptd_normal
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,
)
from preliz.internal.special import mean_and_std
[docs]
class Normal(Continuous):
r"""
Normal distribution.
The pdf of this distribution is
.. math::
f(x \mid \mu, \sigma) =
\frac{1}{\sigma \sqrt{2\pi}}
\exp\left\{ -\frac{1}{2} \left(\frac{x-\mu}{\sigma}\right)^2 \right\}
.. plot::
:context: close-figs
from preliz import Normal, style
style.use('preliz-doc')
mus = [0., 0., -2.]
sigmas = [1, 0.5, 1]
for mu, sigma in zip(mus, sigmas):
Normal(mu, sigma).plot_pdf()
======== ==========================================
Support :math:`x \in \mathbb{R}`
Mean :math:`\mu`
Variance :math:`\sigma^2`
======== ==========================================
Normal distribution has 2 alternative parameterizations. In terms of mean and
sigma (standard deviation), or mean and tau (precision).
The link between the 2 alternatives is given by
.. math::
\tau = \frac{1}{\sigma^2}
Parameters
----------
mu : float
Mean.
sigma : float
Standard deviation (sigma > 0).
tau : float
Precision (tau > 0).
"""
def __init__(self, mu=None, sigma=None, tau=None):
super().__init__()
self.support = (-pt.inf, pt.inf)
self._parametrization(mu, sigma, tau)
def _parametrization(self, mu=None, sigma=None, tau=None):
if all_not_none(sigma, tau):
raise ValueError(
"Incompatible parametrization. Either use mu and sigma, or mu and tau."
)
names = ("mu", "sigma")
self.params_support = ((-pt.inf, pt.inf), (eps, pt.inf))
if tau is not None:
self.tau = tau
sigma = from_precision(tau)
names = ("mu", "tau")
self.mu = mu
self.sigma = sigma
self.param_names = names
if all_not_none(mu, sigma):
self._update(mu, sigma)
def _update(self, mu, sigma):
self.mu = mu # np.float64(mu)
self.sigma = sigma # np.float64(sigma)
self.tau = to_precision(sigma)
if self.param_names[1] == "sigma":
self.params = (self.mu, self.sigma)
elif self.param_names[1] == "tau":
self.params = (self.mu, self.tau)
self.is_frozen = True
def _fit_moments(self, mean, sigma):
self._update(mean, sigma)
def _fit_mle(self, sample):
self._update(*mean_and_std(sample))
[docs]
def pdf(self, x):
return ptd_pdf(x, self.mu, self.sigma)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.mu, self.sigma)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.mu, self.sigma)
[docs]
def sf(self, x):
return ptd_sf(x, self.mu, self.sigma)
[docs]
def isf(self, q):
return ptd_isf(q, self.mu, self.sigma)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.mu, self.sigma)
[docs]
def logcdf(self, x):
return ptd_logcdf(x, self.mu, self.sigma)
[docs]
def logsf(self, x):
return ptd_logsf(x, self.mu, self.sigma)
def logisf(self, q):
return ptd_logisf(q, self.mu, self.sigma)
[docs]
def entropy(self):
return ptd_entropy(self.mu, self.sigma)
[docs]
def mean(self):
return ptd_mean(self.mu, self.sigma)
[docs]
def mode(self):
return ptd_mode(self.mu, self.sigma)
[docs]
def var(self):
return ptd_var(self.mu, self.sigma)
[docs]
def std(self):
return ptd_std(self.mu, self.sigma)
[docs]
def skewness(self):
return ptd_skewness(self.mu, self.sigma)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.mu, self.sigma)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.mu, self.sigma)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.mu, self.sigma)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.mu, self.sigma)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.mu, self.sigma)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.mu, self.sigma, size=size, rng=random_state)
@pytensor_jit
def ptd_pdf(x, mu, sigma):
return ptd_normal.pdf(x, mu, sigma)
@pytensor_jit
def ptd_cdf(x, mu, sigma):
return ptd_normal.cdf(x, mu, sigma)
@pytensor_jit
def ptd_ppf(q, mu, sigma):
return ptd_normal.ppf(q, mu, sigma)
@pytensor_jit
def ptd_sf(x, mu, sigma):
return ptd_normal.sf(x, mu, sigma)
@pytensor_jit
def ptd_isf(q, mu, sigma):
return ptd_normal.isf(q, mu, sigma)
@pytensor_jit
def ptd_logpdf(x, mu, sigma):
return ptd_normal.logpdf(x, mu, sigma)
@pytensor_jit
def ptd_logcdf(x, mu, sigma):
return ptd_normal.logcdf(x, mu, sigma)
@pytensor_jit
def ptd_logsf(x, mu, sigma):
return ptd_normal.logsf(x, mu, sigma)
@pytensor_jit
def ptd_logisf(q, mu, sigma):
return ptd_normal.logisf(q, mu, sigma)
@pytensor_jit
def ptd_entropy(mu, sigma):
return ptd_normal.entropy(mu, sigma)
@pytensor_jit
def ptd_mean(mu, sigma):
return ptd_normal.mean(mu, sigma)
@pytensor_jit
def ptd_mode(mu, sigma):
return ptd_normal.mode(mu, sigma)
@pytensor_jit
def ptd_median(mu, sigma):
return ptd_normal.median(mu, sigma)
@pytensor_jit
def ptd_var(mu, sigma):
return ptd_normal.var(mu, sigma)
@pytensor_jit
def ptd_std(mu, sigma):
return ptd_normal.std(mu, sigma)
@pytensor_jit
def ptd_skewness(mu, sigma):
return ptd_normal.skewness(mu, sigma)
@pytensor_jit
def ptd_kurtosis(mu, sigma):
return ptd_normal.kurtosis(mu, sigma)
@pytensor_jit
def ptd_lmoment1(mu, sigma):
return ptd_normal.lmoment1(mu, sigma)
@pytensor_jit
def ptd_lmoment2(mu, sigma):
return ptd_normal.lmoment2(mu, sigma)
@pytensor_jit
def ptd_lmoment3(mu, sigma):
return ptd_normal.lmoment3(mu, sigma)
@pytensor_jit
def ptd_lmoment4(mu, sigma):
return ptd_normal.lmoment4(mu, sigma)
@pytensor_rng_jit
def ptd_rvs(mu, sigma, size, rng):
return ptd_normal.rvs(mu, sigma, size=size, random_state=rng)
