import numpy as np
from pytensor_distributions import zi_poisson as ptd_zipoisson
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 ZeroInflatedPoisson(Discrete):
R"""
Zero-inflated Poisson distribution.
Often used to model the number of events occurring in a fixed period
of time when the times at which events occur are independent.
The pmf of this distribution is
.. math::
f(x \mid \psi, \mu) = \left\{ \begin{array}{l}
(1-\psi) + \psi e^{-\mu}, \text{if } x = 0 \\
\psi \frac{e^{-\mu}\mu^x}{x!}, \text{if } x=1,2,3,\ldots
\end{array} \right.
.. plot::
:context: close-figs
from preliz import ZeroInflatedPoisson, style
style.use('preliz-doc')
psis = [0.7, 0.4]
mus = [8, 4]
for psi, mu in zip(psis, mus):
ZeroInflatedPoisson(psi, mu).plot_pdf()
======== ================================
Support :math:`x \in \mathbb{N}_0`
Mean :math:`\psi \mu`
Variance :math:`\psi \mu (1+(1-\psi) \mu`
======== ================================
Parameters
----------
psi : float
Expected proportion of Poisson variates (0 < psi < 1)
mu : float
Expected number of occurrences during the given interval
(mu >= 0).
"""
def __init__(self, psi=None, mu=None):
super().__init__()
self.support = (0, np.inf)
self._parametrization(psi, mu)
def _parametrization(self, psi=None, mu=None):
self.psi = psi
self.mu = mu
self.params = (self.psi, self.mu)
self.param_names = ("psi", "mu")
self.params_support = ((eps, 1 - eps), (eps, np.inf))
if all_not_none(psi, mu):
self._update(psi, mu)
def _update(self, psi, mu):
self.psi = np.float64(psi)
self.mu = np.float64(mu)
self.params = (self.psi, self.mu)
self.is_frozen = True
def _fit_moments(self, mean, sigma):
optimize_mean_sigma(self, mean, sigma)
def _fit_mle(self, sample):
optimize_ml(self, sample)
[docs]
def pdf(self, x):
x = np.asarray(x)
result = ptd_pdf(x, self.psi, self.mu)
# Return 0 for negative values and NaN for infinity, consistent with scipy.stats.poisson
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.mu)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.psi, self.mu)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.psi, self.mu)
[docs]
def entropy(self):
return ptd_entropy(self.psi, self.mu)
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def mean(self):
return ptd_mean(self.psi, self.mu)
[docs]
def mode(self):
return ptd_mode(self.psi, self.mu)
[docs]
def var(self):
return ptd_var(self.psi, self.mu)
[docs]
def std(self):
return ptd_std(self.psi, self.mu)
[docs]
def skewness(self):
return ptd_skewness(self.psi, self.mu)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.psi, self.mu)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.psi, self.mu)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.psi, self.mu)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.psi, self.mu)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.psi, self.mu)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.psi, self.mu, size=size, rng=random_state)
@pytensor_jit
def ptd_pdf(x, psi, mu):
return ptd_zipoisson.pdf(x, psi, mu)
@pytensor_jit
def ptd_cdf(x, psi, mu):
return ptd_zipoisson.cdf(x, psi, mu)
@pytensor_jit
def ptd_ppf(q, psi, mu):
return ptd_zipoisson.ppf(q, psi, mu)
@pytensor_jit
def ptd_logpdf(x, psi, mu):
return ptd_zipoisson.logpdf(x, psi, mu)
@pytensor_jit
def ptd_entropy(psi, mu):
return ptd_zipoisson.entropy(psi, mu)
@pytensor_jit
def ptd_mean(psi, mu):
return ptd_zipoisson.mean(psi, mu)
@pytensor_jit
def ptd_mode(psi, mu):
return ptd_zipoisson.mode(psi, mu)
@pytensor_jit
def ptd_median(psi, mu):
return ptd_zipoisson.median(psi, mu)
@pytensor_jit
def ptd_var(psi, mu):
return ptd_zipoisson.var(psi, mu)
@pytensor_jit
def ptd_std(psi, mu):
return ptd_zipoisson.std(psi, mu)
@pytensor_jit
def ptd_skewness(psi, mu):
return ptd_zipoisson.skewness(psi, mu)
@pytensor_jit
def ptd_kurtosis(psi, mu):
return ptd_zipoisson.kurtosis(psi, mu)
@pytensor_jit
def ptd_lmoment1(psi, mu):
return ptd_zipoisson.lmoment1(psi, mu)
@pytensor_jit
def ptd_lmoment2(psi, mu):
return ptd_zipoisson.lmoment2(psi, mu)
@pytensor_jit
def ptd_lmoment3(psi, mu):
return ptd_zipoisson.lmoment3(psi, mu)
@pytensor_jit
def ptd_lmoment4(psi, mu):
return ptd_zipoisson.lmoment4(psi, mu)
@pytensor_rng_jit
def ptd_rvs(psi, mu, size, rng):
return ptd_zipoisson.rvs(psi, mu, size=size, random_state=rng)
