import numpy as np
from pytensor_distributions import zi_negativebinomial as ptd_zinegativebinomial
from preliz.distributions.distributions import Discrete
from preliz.internal.distribution_helper import (
all_not_none,
any_not_none,
eps,
pytensor_jit,
pytensor_rng_jit,
)
from preliz.internal.optimization import optimize_mean_sigma, optimize_ml
[docs]
class ZeroInflatedNegativeBinomial(Discrete):
R"""
Zero-Inflated Negative binomial distribution.
The Zero-inflated version of the Negative Binomial (NB).
The NB distribution describes a Poisson random variable
whose rate parameter is gamma distributed.
The pmf of this distribution is
.. math::
f(x \mid \psi, \mu, \alpha) = \left\{
\begin{array}{l}
(1-\psi) + \psi \left (
\frac{\alpha}{\alpha+\mu}
\right) ^\alpha, \text{if } x = 0 \\
\psi \frac{\Gamma(x+\alpha)}{x! \Gamma(\alpha)} \left (
\frac{\alpha}{\mu+\alpha}
\right)^\alpha \left(
\frac{\mu}{\mu+\alpha}
\right)^x, \text{if } x=1,2,3,\ldots
\end{array}
\right.
.. plot::
:context: close-figs
from preliz import ZeroInflatedNegativeBinomial, style
style.use('preliz-doc')
psis = [0.7, 0.7]
mus = [2, 8]
alphas = [2, 4]
for psi, mu, alpha in zip(psis, mus, alphas):
ZeroInflatedNegativeBinomial(psi, mu=mu, alpha=alpha).plot_pdf(support=(0,25))
======== ===================================
Support :math:`x \in \mathbb{N}_0`
Mean :math:`\psi\mu`
Variance :math:`\psi \left(\frac{\mu^2}{\alpha}\right) + \psi \mu + \psi \mu^2 - \psi^2 \mu^2`
======== ==================================
The zero inflated negative binomial distribution can be parametrized
either in terms of mu and alpha, or in terms of n and p.
The link between the parametrizations is given by
.. math::
\mu &= \frac{n(1-p)}{p} \\
\alpha &= n
Parameters
----------
psi : float
Expected proportion of NegativeBinomial variates (0 < psi < 1)
mu : float
Poisson distribution parameter (mu > 0).
alpha : float
Gamma distribution parameter (alpha > 0).
p : float
Alternative probability of success in each trial (0 < p < 1).
n : float
Alternative number of target success trials (n > 0)
"""
def __init__(self, psi=None, mu=None, alpha=None, p=None, n=None):
super().__init__()
self.support = (0, np.inf)
self._parametrization(psi, mu, alpha, p, n)
def _parametrization(self, psi=None, mu=None, alpha=None, p=None, n=None):
if any_not_none(mu, alpha) and any_not_none(p, n):
raise ValueError(
"Incompatible parametrization. Either use psi, mu and alpha, or psi, p and n."
)
self.psi = psi
self.param_names = ("psi", "mu", "alpha")
self.params_support = ((eps, 1 - eps), (eps, np.inf), (eps, np.inf))
if any_not_none(p, n):
self.p = p
self.n = n
self.param_names = ("psi", "p", "n")
if all_not_none(p, n):
mu, alpha = self._from_p_n(p, n)
self.mu = mu
self.alpha = alpha
self.params = (self.psi, self.mu, self.alpha)
if all_not_none(mu, alpha):
self._update(psi, mu, alpha)
def _from_p_n(self, p, n):
alpha = n
mu = n * (1 / p - 1)
return mu, alpha
def _to_p_n(self, mu, alpha):
p = alpha / (mu + alpha)
n = alpha
return p, n
def _update(self, psi, mu, alpha):
self.psi = np.float64(psi)
self.mu = np.float64(mu)
self.alpha = np.float64(alpha)
self.p, self.n = self._to_p_n(self.mu, self.alpha)
if self.param_names[1] == "mu":
self.params = (self.psi, self.mu, self.alpha)
elif self.param_names[1] == "p":
self.params = (self.psi, self.p, 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 negative values and NaN for infinity, consistent with scipy.stats.nbinom
result = np.where(x < 0, 0, result)
result = np.where(~np.isfinite(x), np.nan, 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_zinegativebinomial.pdf(x, psi, n, p)
@pytensor_jit
def ptd_cdf(x, psi, n, p):
return ptd_zinegativebinomial.cdf(x, psi, n, p)
@pytensor_jit
def ptd_ppf(q, psi, n, p):
return ptd_zinegativebinomial.ppf(q, psi, n, p)
@pytensor_jit
def ptd_logpdf(x, psi, n, p):
return ptd_zinegativebinomial.logpdf(x, psi, n, p)
@pytensor_jit
def ptd_entropy(psi, n, p):
return ptd_zinegativebinomial.entropy(psi, n, p)
@pytensor_jit
def ptd_mean(psi, n, p):
return ptd_zinegativebinomial.mean(psi, n, p)
@pytensor_jit
def ptd_mode(psi, n, p):
return ptd_zinegativebinomial.mode(psi, n, p)
@pytensor_jit
def ptd_median(psi, n, p):
return ptd_zinegativebinomial.median(psi, n, p)
@pytensor_jit
def ptd_var(psi, n, p):
return ptd_zinegativebinomial.var(psi, n, p)
@pytensor_jit
def ptd_std(psi, n, p):
return ptd_zinegativebinomial.std(psi, n, p)
@pytensor_jit
def ptd_skewness(psi, n, p):
return ptd_zinegativebinomial.skewness(psi, n, p)
@pytensor_jit
def ptd_kurtosis(psi, n, p):
return ptd_zinegativebinomial.kurtosis(psi, n, p)
@pytensor_jit
def ptd_lmoment1(psi, n, p):
return ptd_zinegativebinomial.lmoment1(psi, n, p)
@pytensor_jit
def ptd_lmoment2(psi, n, p):
return ptd_zinegativebinomial.lmoment2(psi, n, p)
@pytensor_jit
def ptd_lmoment3(psi, n, p):
return ptd_zinegativebinomial.lmoment3(psi, n, p)
@pytensor_jit
def ptd_lmoment4(psi, n, p):
return ptd_zinegativebinomial.lmoment4(psi, n, p)
@pytensor_rng_jit
def ptd_rvs(psi, n, p, size, rng):
return ptd_zinegativebinomial.rvs(psi, n, p, size=size, random_state=rng)
