import numpy as np
from pytensor_distributions import truncatednormal as ptd_truncatednormal
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
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class TruncatedNormal(Continuous):
r"""
TruncatedNormal distribution.
The pdf of this distribution is
.. math::
f(x;\mu ,\sigma ,a,b)={\frac {\phi ({\frac {x-\mu }{\sigma }})}{
\sigma \left(\Phi ({\frac {b-\mu }{\sigma }})-\Phi ({\frac {a-\mu }{\sigma }})\right)}}
.. plot::
:context: close-figs
from preliz import TruncatedNormal, style
style.use('preliz-doc')
mus = [0., 0., 0.]
sigmas = [3.,5.,7.]
lowers = [-3, -5, -5]
uppers = [7, 5, 4]
for mu, sigma, lower, upper in zip(mus, sigmas,lowers,uppers):
TruncatedNormal(mu, sigma, lower, upper).plot_pdf(support=(-10,10))
======== ==========================================
Support :math:`x \in [a, b]`
Mean :math:`\mu +{\frac {\phi (\alpha )-\phi (\beta )}{Z}}\sigma`
Variance .. math::
\sigma ^{2}\left[1+{\frac {\alpha \phi (\alpha )-\beta \phi (\beta )}{Z}}-
\left({\frac {\phi (\alpha )-\phi (\beta )}{Z}}\right)^{2}\right]
======== ==========================================
Parameters
----------
mu : float
Mean.
sigma : float
Standard deviation (sigma > 0)
lower: float
Lower limit.
upper: float
Upper limit (upper > lower).
"""
def __init__(self, mu=None, sigma=None, lower=None, upper=None):
super().__init__()
self._parametrization(mu, sigma, lower, upper)
def _parametrization(self, mu=None, sigma=None, lower=None, upper=None):
self.mu = mu
self.sigma = sigma
self.lower = lower
self.upper = upper
self.params = (self.mu, self.sigma, self.lower, self.upper)
self.param_names = ("mu", "sigma", "lower", "upper")
self.params_support = (
(-np.inf, np.inf),
(eps, np.inf),
(-np.inf, np.inf),
(-np.inf, np.inf),
)
if lower is None:
self.lower = -np.inf
if upper is None:
self.upper = np.inf
self.support = (self.lower, self.upper)
if all_not_none(mu, sigma, lower, upper):
self._update(mu, sigma, lower, upper)
def _update(self, mu, sigma, lower=None, upper=None):
if lower is not None:
self.lower = np.float64(lower)
if upper is not None:
self.upper = np.float64(upper)
self.mu = np.float64(mu)
self.sigma = np.float64(sigma)
self.params = (self.mu, self.sigma, self.lower, self.upper)
self.support = (self.lower, self.upper)
self.is_frozen = True
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def pdf(self, x):
return ptd_pdf(x, self.mu, self.sigma, self.lower, self.upper)
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def cdf(self, x):
return ptd_cdf(x, self.mu, self.sigma, self.lower, self.upper)
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def ppf(self, q):
return ptd_ppf(q, self.mu, self.sigma, self.lower, self.upper)
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def logpdf(self, x):
return ptd_logpdf(x, self.mu, self.sigma, self.lower, self.upper)
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def entropy(self):
return ptd_entropy(self.mu, self.sigma, self.lower, self.upper)
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def mean(self):
return ptd_mean(self.mu, self.sigma, self.lower, self.upper)
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def mode(self):
return ptd_mode(self.mu, self.sigma, self.lower, self.upper)
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def var(self):
return ptd_var(self.mu, self.sigma, self.lower, self.upper)
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def std(self):
return ptd_std(self.mu, self.sigma, self.lower, self.upper)
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def skewness(self):
return ptd_skewness(self.mu, self.sigma, self.lower, self.upper)
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def kurtosis(self):
return ptd_kurtosis(self.mu, self.sigma, self.lower, self.upper)
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def lmoment1(self):
return ptd_lmoment1(self.mu, self.sigma, self.lower, self.upper)
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def lmoment2(self):
return ptd_lmoment2(self.mu, self.sigma, self.lower, self.upper)
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def lmoment3(self):
return ptd_lmoment3(self.mu, self.sigma, self.lower, self.upper)
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def lmoment4(self):
return ptd_lmoment4(self.mu, self.sigma, self.lower, self.upper)
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def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.mu, self.sigma, self.lower, self.upper, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
# Assume gaussian
self._update(mean, sigma)
def _fit_mle(self, sample):
self._update(None, None, np.min(sample), np.max(sample))
optimize_ml(self, sample)
@pytensor_jit
def ptd_pdf(x, mu, sigma, lower, upper):
return ptd_truncatednormal.pdf(x, mu, sigma, lower, upper)
@pytensor_jit
def ptd_cdf(x, mu, sigma, lower, upper):
return ptd_truncatednormal.cdf(x, mu, sigma, lower, upper)
@pytensor_jit
def ptd_ppf(q, mu, sigma, lower, upper):
return ptd_truncatednormal.ppf(q, mu, sigma, lower, upper)
@pytensor_jit
def ptd_logpdf(x, mu, sigma, lower, upper):
return ptd_truncatednormal.logpdf(x, mu, sigma, lower, upper)
@pytensor_jit
def ptd_entropy(mu, sigma, lower, upper):
return ptd_truncatednormal.entropy(mu, sigma, lower, upper)
@pytensor_jit
def ptd_mean(mu, sigma, lower, upper):
return ptd_truncatednormal.mean(mu, sigma, lower, upper)
@pytensor_jit
def ptd_mode(mu, sigma, lower, upper):
return ptd_truncatednormal.mode(mu, sigma, lower, upper)
@pytensor_jit
def ptd_median(mu, sigma, lower, upper):
return ptd_truncatednormal.median(mu, sigma, lower, upper)
@pytensor_jit
def ptd_var(mu, sigma, lower, upper):
return ptd_truncatednormal.var(mu, sigma, lower, upper)
@pytensor_jit
def ptd_std(mu, sigma, lower, upper):
return ptd_truncatednormal.std(mu, sigma, lower, upper)
@pytensor_jit
def ptd_skewness(mu, sigma, lower, upper):
return ptd_truncatednormal.skewness(mu, sigma, lower, upper)
@pytensor_jit
def ptd_kurtosis(mu, sigma, lower, upper):
return ptd_truncatednormal.kurtosis(mu, sigma, lower, upper)
@pytensor_jit
def ptd_lmoment1(mu, sigma, lower, upper):
return ptd_truncatednormal.lmoment1(mu, sigma, lower, upper)
@pytensor_jit
def ptd_lmoment2(mu, sigma, lower, upper):
return ptd_truncatednormal.lmoment2(mu, sigma, lower, upper)
@pytensor_jit
def ptd_lmoment3(mu, sigma, lower, upper):
return ptd_truncatednormal.lmoment3(mu, sigma, lower, upper)
@pytensor_jit
def ptd_lmoment4(mu, sigma, lower, upper):
return ptd_truncatednormal.lmoment4(mu, sigma, lower, upper)
@pytensor_rng_jit
def ptd_rvs(mu, sigma, lower, upper, size, rng):
return ptd_truncatednormal.rvs(mu, sigma, lower, upper, size=size, random_state=rng)
