Source code for preliz.distributions.geometric
import numpy as np
from pytensor_distributions import geometric as ptd_geometric
from preliz.distributions.distributions import Discrete
from preliz.internal.distribution_helper import eps, pytensor_jit, pytensor_rng_jit
[docs]
class Geometric(Discrete):
R"""
Geometric distribution.
The probability that the first success in a sequence of Bernoulli trials
occurs on the x'th trial.
The pmf of this distribution is
.. math::
f(x \mid p) = p(1-p)^{x-1}
.. plot::
:context: close-figs
from preliz import Geometric, style
style.use('preliz-doc')
for p in [0.1, 0.25, 0.75]:
Geometric(p).plot_pdf(support=(1,10))
======== =============================
Support :math:`x \in \mathbb{N}_{>0}`
Mean :math:`\dfrac{1}{p}`
Variance :math:`\dfrac{1 - p}{p^2}`
======== =============================
Parameters
----------
p : float
Probability of success on an individual trial (0 < p <= 1).
"""
def __init__(self, p=None):
super().__init__()
self.support = (1, np.inf)
self._parametrization(p)
def _parametrization(self, p=None):
self.p = p
self.param_names = "p"
self.params_support = ((eps, 1),)
if self.p is not None:
self._update(self.p)
def _update(self, p):
self.p = np.float64(p)
self.params = (self.p,)
self.is_frozen = True
[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)
[docs]
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)
def _fit_moments(self, mean, sigma):
p = 1 / mean
self._update(p)
def _fit_mle(self, sample):
p = 1 / np.mean(sample)
self._update(p)
@pytensor_jit
def ptd_pdf(x, p):
return ptd_geometric.pdf(x, p)
@pytensor_jit
def ptd_cdf(x, p):
return ptd_geometric.cdf(x, p)
@pytensor_jit
def ptd_ppf(q, p):
return ptd_geometric.ppf(q, p)
@pytensor_jit
def ptd_logpdf(x, p):
return ptd_geometric.logpdf(x, p)
@pytensor_jit
def ptd_entropy(p):
return ptd_geometric.entropy(p)
@pytensor_jit
def ptd_mean(p):
return ptd_geometric.mean(p)
@pytensor_jit
def ptd_mode(p):
return ptd_geometric.mode(p)
@pytensor_jit
def ptd_median(p):
return ptd_geometric.median(p)
@pytensor_jit
def ptd_var(p):
return ptd_geometric.var(p)
@pytensor_jit
def ptd_std(p):
return ptd_geometric.std(p)
@pytensor_jit
def ptd_skewness(p):
return ptd_geometric.skewness(p)
@pytensor_jit
def ptd_kurtosis(p):
return ptd_geometric.kurtosis(p)
@pytensor_jit
def ptd_lmoment1(p):
return ptd_geometric.lmoment1(p)
@pytensor_jit
def ptd_lmoment2(p):
return ptd_geometric.lmoment2(p)
@pytensor_jit
def ptd_lmoment3(p):
return ptd_geometric.lmoment3(p)
@pytensor_jit
def ptd_lmoment4(p):
return ptd_geometric.lmoment4(p)
@pytensor_rng_jit
def ptd_rvs(p, size, rng):
return ptd_geometric.rvs(p, size=size, random_state=rng)
