"""BetaBinomial probability distribution."""
import numpy as np
from pytensor_distributions import betabinomial as ptd_betabinomial
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 BetaBinomial(Discrete):
R"""
Beta-binomial distribution.
Equivalent to binomial random variable with success probability
drawn from a beta distribution.
The pmf of this distribution is
.. math::
f(x \mid \alpha, \beta, n) =
\binom{n}{x}
\frac{B(x + \alpha, n - x + \beta)}{B(\alpha, \beta)}
.. plot::
:context: close-figs
from preliz import BetaBinomial, style
style.use('preliz-doc')
alphas = [0.5, 1, 2.3]
betas = [0.5, 1, 2]
n = 10
for a, b in zip(alphas, betas):
BetaBinomial(a, b, n).plot_pdf()
======== =================================================================
Support :math:`x \in \{0, 1, \ldots, n\}`
Mean :math:`n \dfrac{\alpha}{\alpha + \beta}`
Variance :math:`\dfrac{n \alpha \beta (\alpha+\beta+n)}{(\alpha+\beta)^2 (\alpha+\beta+1)}`
======== =================================================================
Parameters
----------
n : int
Number of Bernoulli trials (n >= 0).
alpha : float
alpha > 0.
beta : float
beta > 0.
"""
def __init__(self, alpha=None, beta=None, n=None):
super().__init__()
self.support = (0, np.inf)
self._parametrization(alpha, beta, n)
def _parametrization(self, alpha=None, beta=None, n=None):
self.alpha = alpha
self.beta = beta
self.n = n
self.params = (self.alpha, self.beta, self.n)
self.param_names = ("alpha", "beta", "n")
self.params_support = ((eps, np.inf), (eps, np.inf), (eps, np.inf))
if all_not_none(alpha, beta, n):
self._update(alpha, beta, n)
def _update(self, alpha, beta, n):
self.alpha = np.float64(alpha)
self.beta = np.float64(beta)
self.n = np.int64(n)
self.params = (self.alpha, self.beta, self.n)
self.support = (0, self.n)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.n, self.alpha, self.beta)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.n, self.alpha, self.beta)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.n, self.alpha, self.beta)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.n, self.alpha, self.beta)
[docs]
def entropy(self):
return ptd_entropy(self.n, self.alpha, self.beta)
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def mean(self):
return ptd_mean(self.n, self.alpha, self.beta)
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def mode(self):
return ptd_mode(self.n, self.alpha, self.beta)
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def var(self):
return ptd_var(self.n, self.alpha, self.beta)
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def std(self):
return ptd_std(self.n, self.alpha, self.beta)
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def skewness(self):
return ptd_skewness(self.n, self.alpha, self.beta)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.n, self.alpha, self.beta)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.n, self.alpha, self.beta)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.n, self.alpha, self.beta)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.n, self.alpha, self.beta)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.n, self.alpha, self.beta)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.n, self.alpha, self.beta, 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, n, alpha, beta):
return ptd_betabinomial.pdf(x, n, alpha, beta)
@pytensor_jit
def ptd_cdf(x, n, alpha, beta):
return ptd_betabinomial.cdf(x, n, alpha, beta)
@pytensor_jit
def ptd_ppf(q, n, alpha, beta):
return ptd_betabinomial.ppf(q, n, alpha, beta)
@pytensor_jit
def ptd_logpdf(x, n, alpha, beta):
return ptd_betabinomial.logpdf(x, n, alpha, beta)
@pytensor_jit
def ptd_entropy(n, alpha, beta):
return ptd_betabinomial.entropy(n, alpha, beta)
@pytensor_jit
def ptd_mean(n, alpha, beta):
return ptd_betabinomial.mean(n, alpha, beta)
@pytensor_jit
def ptd_mode(n, alpha, beta):
return ptd_betabinomial.mode(n, alpha, beta)
@pytensor_jit
def ptd_median(n, alpha, beta):
return ptd_betabinomial.median(n, alpha, beta)
@pytensor_jit
def ptd_var(n, alpha, beta):
return ptd_betabinomial.var(n, alpha, beta)
@pytensor_jit
def ptd_std(n, alpha, beta):
return ptd_betabinomial.std(n, alpha, beta)
@pytensor_jit
def ptd_skewness(n, alpha, beta):
return ptd_betabinomial.skewness(n, alpha, beta)
@pytensor_jit
def ptd_kurtosis(n, alpha, beta):
return ptd_betabinomial.kurtosis(n, alpha, beta)
@pytensor_jit
def ptd_lmoment1(n, alpha, beta):
return ptd_betabinomial.lmoment1(n, alpha, beta)
@pytensor_jit
def ptd_lmoment2(n, alpha, beta):
return ptd_betabinomial.lmoment2(n, alpha, beta)
@pytensor_jit
def ptd_lmoment3(n, alpha, beta):
return ptd_betabinomial.lmoment3(n, alpha, beta)
@pytensor_jit
def ptd_lmoment4(n, alpha, beta):
return ptd_betabinomial.lmoment4(n, alpha, beta)
@pytensor_rng_jit
def ptd_rvs(n, alpha, beta, size, rng):
return ptd_betabinomial.rvs(n, alpha, beta, size=size, random_state=rng)
