import numpy as np
from pytensor_distributions import discreteweibull as ptd_discreteweibull
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 DiscreteWeibull(Discrete):
R"""
Discrete Weibull distribution.
The pmf of this distribution is
.. math::
f(x \mid q, \beta) = q^{x^{\beta}} - q^{(x+1)^{\beta}}
.. plot::
:context: close-figs
from preliz import DiscreteWeibull, style
style.use('preliz-doc')
qs = [0.1, 0.9, 0.9]
betas = [0.5, 0.5, 2]
for q, b in zip(qs, betas):
DiscreteWeibull(q, b).plot_pdf(support=(0,10))
======== ===============================================
Support :math:`x \in \mathbb{N}_0`
Mean :math:`\mu = \sum_{x = 1}^{\infty} q^{x^{\beta}}`
Variance :math:`2 \sum_{x = 1}^{\infty} x q^{x^{\beta}} - \mu - \mu^2`
======== ===============================================
Parameters
----------
q: float
Shape parameter (0 < q < 1).
beta: float
Shape parameter (beta > 0).
"""
def __init__(self, q=None, beta=None):
super().__init__()
self.support = (0, np.inf)
self._parametrization(q, beta)
def _parametrization(self, q=None, beta=None):
self.q = q
self.beta = beta
self.params = (self.q, self.beta)
self.param_names = ("q", "beta")
self.params_support = ((eps, 1 - eps), (eps, np.inf))
if all_not_none(q, beta):
self._update(q, beta)
def _update(self, q, beta):
self.q = np.float64(q)
self.beta = np.float64(beta)
self.params = (self.q, self.beta)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.q, self.beta)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.q, self.beta)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.q, self.beta)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.q, self.beta)
[docs]
def entropy(self):
return ptd_entropy(self.q, self.beta)
[docs]
def mean(self):
return ptd_mean(self.q, self.beta)
[docs]
def var(self):
return ptd_var(self.q, self.beta)
[docs]
def std(self):
return ptd_std(self.q, self.beta)
[docs]
def skewness(self):
return ptd_skewness(self.q, self.beta)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.q, self.beta)
[docs]
def mode(self):
return ptd_mode(self.q, self.beta)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.q, 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, q, beta):
return ptd_discreteweibull.pdf(x, q, beta)
@pytensor_jit
def ptd_cdf(x, q, beta):
return ptd_discreteweibull.cdf(x, q, beta)
@pytensor_jit
def ptd_ppf(p, q, beta):
return ptd_discreteweibull.ppf(p, q, beta)
@pytensor_jit
def ptd_logpdf(x, q, beta):
return ptd_discreteweibull.logpdf(x, q, beta)
@pytensor_jit
def ptd_entropy(q, beta):
return ptd_discreteweibull.entropy(q, beta)
@pytensor_jit
def ptd_mean(q, beta):
return ptd_discreteweibull.mean(q, beta)
@pytensor_jit
def ptd_mode(q, beta):
return ptd_discreteweibull.mode(q, beta)
@pytensor_jit
def ptd_median(q, beta):
return ptd_discreteweibull.median(q, beta)
@pytensor_jit
def ptd_var(q, beta):
return ptd_discreteweibull.var(q, beta)
@pytensor_jit
def ptd_std(q, beta):
return ptd_discreteweibull.std(q, beta)
@pytensor_jit
def ptd_skewness(q, beta):
return ptd_discreteweibull.skewness(q, beta)
@pytensor_jit
def ptd_kurtosis(q, beta):
return ptd_discreteweibull.kurtosis(q, beta)
@pytensor_rng_jit
def ptd_rvs(q, beta, size, rng):
return ptd_discreteweibull.rvs(q, beta, size=size, random_state=rng)
