import numpy as np
from pytensor_distributions import bernoulli as ptd_bernoulli
from preliz.distributions.distributions import Discrete
from preliz.internal.distribution_helper import all_not_none, eps, pytensor_jit, pytensor_rng_jit
from preliz.internal.optimization import optimize_ml
from preliz.internal.special import expit, logit
[docs]
class Bernoulli(Discrete):
R"""Bernoulli distribution.
The Bernoulli distribution describes the probability of successes (x=1) and failures (x=0).
The pmf of this distribution is
.. math::
f(x \mid p) = p^{x} (1-p)^{1-x}
.. plot::
:context: close-figs
from preliz import Bernoulli, style
style.use('preliz-doc')
for p in [0, 0.5, 0.8]:
Bernoulli(p).plot_pdf()
======== ======================
Support :math:`x \in \{0, 1\}`
Mean :math:`p`
Variance :math:`p (1 - p)`
======== ======================
The Bernoulli distribution has 2 alternative parametrizations. In terms of p or logit_p.
The link between the 2 alternatives is given by
.. math::
logit(p) = ln(\frac{p}{1-p})
Parameters
----------
p : float
Probability of success (0 < p < 1).
logit_p : float
Alternative log odds for the probability of success.
"""
def __init__(self, p=None, logit_p=None):
super().__init__()
self.support = (0, 1)
self._parametrization(p, logit_p)
def _parametrization(self, p=None, logit_p=None):
if all_not_none(p, logit_p):
raise ValueError("Incompatible parametrization. Either use p or logit_p.")
self.param_names = "p"
self.params_support = ((eps, 1),)
if logit_p is not None:
p = self._from_logit_p(logit_p)
self.param_names = ("logit_p",)
self.p = p
self.logit_p = logit_p
if self.p is not None:
self._update(self.p)
def _from_logit_p(self, logit_p):
return expit(logit_p)
def _to_logit_p(self, p):
return logit(p)
def _update(self, p):
self.p = np.float64(p)
self._q = 1 - self.p
self.logit_p = self._to_logit_p(p)
if self.param_names[0] == "p":
self.params = (self.p,)
elif self.param_names[0] == "logit_p":
self.params = (self.logit_p,)
self.is_frozen = True
def _fit_moments(self, mean, sigma):
self._update(mean)
def _fit_mle(self, sample):
optimize_ml(self, sample)
[docs]
def pdf(self, x):
return ptd_pdf(x, self.p)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.p)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.p)
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def logpdf(self, x):
return ptd_logpdf(x, self.p)
[docs]
def entropy(self):
return ptd_entropy(self.p)
[docs]
def mean(self):
return ptd_mean(self.p)
[docs]
def mode(self):
return ptd_mode(self.p)
[docs]
def var(self):
return ptd_var(self.p)
[docs]
def std(self):
return ptd_std(self.p)
[docs]
def skewness(self):
return ptd_skewness(self.p)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.p)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.p)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.p)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.p)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.p)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.p, size=size, rng=random_state)
@pytensor_jit
def ptd_pdf(x, p):
return ptd_bernoulli.pdf(x, p)
@pytensor_jit
def ptd_cdf(x, p):
return ptd_bernoulli.cdf(x, p)
@pytensor_jit
def ptd_ppf(q, p):
return ptd_bernoulli.ppf(q, p)
@pytensor_jit
def ptd_logpdf(x, p):
return ptd_bernoulli.logpdf(x, p)
@pytensor_jit
def ptd_entropy(p):
return ptd_bernoulli.entropy(p)
@pytensor_jit
def ptd_mean(p):
return ptd_bernoulli.mean(p)
@pytensor_jit
def ptd_mode(p):
return ptd_bernoulli.mode(p)
@pytensor_jit
def ptd_median(p):
return ptd_bernoulli.median(p)
@pytensor_jit
def ptd_var(p):
return ptd_bernoulli.var(p)
@pytensor_jit
def ptd_std(p):
return ptd_bernoulli.std(p)
@pytensor_jit
def ptd_skewness(p):
return ptd_bernoulli.skewness(p)
@pytensor_jit
def ptd_kurtosis(p):
return ptd_bernoulli.kurtosis(p)
@pytensor_jit
def ptd_lmoment1(p):
return ptd_bernoulli.lmoment1(p)
@pytensor_jit
def ptd_lmoment2(p):
return ptd_bernoulli.lmoment2(p)
@pytensor_jit
def ptd_lmoment3(p):
return ptd_bernoulli.lmoment3(p)
@pytensor_jit
def ptd_lmoment4(p):
return ptd_bernoulli.lmoment4(p)
@pytensor_rng_jit
def ptd_rvs(p, size, rng):
return ptd_bernoulli.rvs(p, size=size, random_state=rng)
