import numpy as np
from pytensor_distributions import zi_binomial as ptd_zibinomial
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_mean_sigma, optimize_ml
[docs]
class ZeroInflatedBinomial(Discrete):
R"""
Zero-inflated Binomial distribution.
The pmf of this distribution is
.. math::
f(x \mid \psi, n, p) = \left\{ \begin{array}{l}
(1-\psi) + \psi (1-p)^{n}, \text{if } x = 0 \\
\psi {n \choose x} p^x (1-p)^{n-x}, \text{if } x=1,2,3,\ldots,n
\end{array} \right.
.. plot::
:context: close-figs
from preliz import ZeroInflatedBinomial, style
style.use('preliz-doc')
ns = [10, 20]
ps = [0.5, 0.7]
psis = [0.7, 0.4]
for psi, n, p in zip(ns, ps, psis):
ZeroInflatedBinomial(psi, n, p).plot_pdf(support=(0,25))
======== ==========================
Support :math:`x \in \mathbb{N}_0`
Mean :math:`\psi n p`
Variance :math:`\psi n p (1 - p) + n^2 p^2 (\psi - \psi^2)`
======== ==========================
Parameters
----------
psi : float
Expected proportion of Binomial variates (0 < psi < 1)
n : int
Number of Bernoulli trials (n >= 0).
p : float
Probability of success in each trial (0 < p < 1).
"""
def __init__(self, psi=None, n=None, p=None):
super().__init__()
self.support = (0, np.inf)
self._parametrization(psi, n, p)
def _parametrization(self, psi=None, n=None, p=None):
self.psi = psi
self.n = n
self.p = p
self.params = (self.psi, self.n, self.p)
self.param_names = ("psi", "n", "p")
self.params_support = ((eps, 1 - eps), (eps, np.inf), (eps, 1 - eps))
if all_not_none(psi, n, p):
self._update(psi, n, p)
def _update(self, psi, n, p):
self.psi = np.float64(psi)
self.n = np.int64(n)
self.p = np.float64(p)
self.params = (self.psi, self.n, self.p)
if self.psi == 0:
self.support = (0, 0)
else:
self.support = (0, self.n)
self.is_frozen = True
[docs]
def pdf(self, x):
x = np.asarray(x)
result = ptd_pdf(x, self.psi, self.n, self.p)
# Return 0 for values outside support or infinity, consistent with scipy.stats.binom
result = np.where((x < 0) | (x > self.n) | ~np.isfinite(x), 0, result)
return result
[docs]
def cdf(self, x):
return ptd_cdf(x, self.psi, self.n, self.p)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.psi, self.n, self.p)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.psi, self.n, self.p)
[docs]
def entropy(self):
return ptd_entropy(self.psi, self.n, self.p)
[docs]
def mean(self):
return ptd_mean(self.psi, self.n, self.p)
[docs]
def mode(self):
return ptd_mode(self.psi, self.n, self.p)
[docs]
def var(self):
return ptd_var(self.psi, self.n, self.p)
[docs]
def std(self):
return ptd_std(self.psi, self.n, self.p)
[docs]
def skewness(self):
return ptd_skewness(self.psi, self.n, self.p)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.psi, self.n, self.p)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.psi, self.n, self.p)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.psi, self.n, self.p)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.psi, self.n, self.p)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.psi, self.n, self.p)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.psi, self.n, self.p, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
optimize_mean_sigma(self, mean, sigma)
def _fit_mle(self, sample):
optimize_ml(self, sample)
@pytensor_jit
def ptd_pdf(x, psi, n, p):
return ptd_zibinomial.pdf(x, psi, n, p)
@pytensor_jit
def ptd_cdf(x, psi, n, p):
return ptd_zibinomial.cdf(x, psi, n, p)
@pytensor_jit
def ptd_ppf(q, psi, n, p):
return ptd_zibinomial.ppf(q, psi, n, p)
@pytensor_jit
def ptd_logpdf(x, psi, n, p):
return ptd_zibinomial.logpdf(x, psi, n, p)
@pytensor_jit
def ptd_entropy(psi, n, p):
return ptd_zibinomial.entropy(psi, n, p)
@pytensor_jit
def ptd_mean(psi, n, p):
return ptd_zibinomial.mean(psi, n, p)
@pytensor_jit
def ptd_mode(psi, n, p):
return ptd_zibinomial.mode(psi, n, p)
@pytensor_jit
def ptd_median(psi, n, p):
return ptd_zibinomial.median(psi, n, p)
@pytensor_jit
def ptd_var(psi, n, p):
return ptd_zibinomial.var(psi, n, p)
@pytensor_jit
def ptd_std(psi, n, p):
return ptd_zibinomial.std(psi, n, p)
@pytensor_jit
def ptd_skewness(psi, n, p):
return ptd_zibinomial.skewness(psi, n, p)
@pytensor_jit
def ptd_kurtosis(psi, n, p):
return ptd_zibinomial.kurtosis(psi, n, p)
@pytensor_jit
def ptd_lmoment1(psi, n, p):
return ptd_zibinomial.lmoment1(psi, n, p)
@pytensor_jit
def ptd_lmoment2(psi, n, p):
return ptd_zibinomial.lmoment2(psi, n, p)
@pytensor_jit
def ptd_lmoment3(psi, n, p):
return ptd_zibinomial.lmoment3(psi, n, p)
@pytensor_jit
def ptd_lmoment4(psi, n, p):
return ptd_zibinomial.lmoment4(psi, n, p)
@pytensor_rng_jit
def ptd_rvs(psi, n, p, size, rng):
return ptd_zibinomial.rvs(psi, n, p, size=size, random_state=rng)
