import numpy as np
from pytensor_distributions import weibull as ptd_weibull
from preliz.distributions.distributions import Continuous
from preliz.internal.distribution_helper import all_not_none, eps, pytensor_jit, pytensor_rng_jit
from preliz.internal.optimization import optimize_ml
from preliz.internal.special import (
garcia_approximation,
mean_and_std,
)
[docs]
class Weibull(Continuous):
r"""
Weibull distribution.
The pdf of this distribution is
.. math::
f(x \mid \alpha, \beta) =
\frac{\alpha x^{\alpha - 1}
\exp(-(\frac{x}{\beta})^{\alpha})}{\beta^\alpha}
.. plot::
:context: close-figs
from preliz import Weibull, style
style.use('preliz-doc')
alphas = [1., 2, 5.]
betas = [1., 1., 2.]
for a, b in zip(alphas, betas):
Weibull(a, b).plot_pdf(support=(0,5))
======== ====================================================
Support :math:`x \in [0, \infty)`
Mean :math:`\beta \Gamma(1 + \frac{1}{\alpha})`
Variance :math:`\beta^2 \Gamma(1 + \frac{2}{\alpha} - \mu^2/\beta^2)`
======== ====================================================
Parameters
----------
alpha : float
Shape parameter (alpha > 0).
beta : float
Scale parameter (beta > 0).
"""
def __init__(self, alpha=None, beta=None):
super().__init__()
self.support = (0, np.inf)
self._parametrization(alpha, beta)
def _parametrization(self, alpha=None, beta=None):
self.alpha = alpha
self.beta = beta
self.param_names = ("alpha", "beta")
self.params_support = ((eps, np.inf), (eps, np.inf))
if all_not_none(alpha, beta):
self._update(alpha, beta)
def _update(self, alpha, beta):
self.alpha = np.float64(alpha)
self.beta = np.float64(beta)
self.params = (self.alpha, self.beta)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.alpha, self.beta)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.alpha, self.beta)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.alpha, self.beta)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.alpha, self.beta)
[docs]
def entropy(self):
return ptd_entropy(self.alpha, self.beta)
[docs]
def mean(self):
return ptd_mean(self.alpha, self.beta)
[docs]
def mode(self):
return ptd_mode(self.alpha, self.beta)
[docs]
def var(self):
return ptd_var(self.alpha, self.beta)
[docs]
def std(self):
return ptd_std(self.alpha, self.beta)
[docs]
def skewness(self):
return ptd_skewness(self.alpha, self.beta)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.alpha, self.beta)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.alpha, self.beta)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.alpha, self.beta)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.alpha, self.beta)
[docs]
def lmoment4(self):
return ptd_lmoment4(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.alpha, self.beta, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
alpha, beta = garcia_approximation(mean, sigma)
self._update(alpha, beta)
def _fit_mle(self, sample):
mean, std = mean_and_std(sample)
self._fit_moments(mean, std)
optimize_ml(self, sample)
@pytensor_jit
def ptd_pdf(x, alpha, beta):
return ptd_weibull.pdf(x, alpha, beta)
@pytensor_jit
def ptd_cdf(x, alpha, beta):
return ptd_weibull.cdf(x, alpha, beta)
@pytensor_jit
def ptd_ppf(q, alpha, beta):
return ptd_weibull.ppf(q, alpha, beta)
@pytensor_jit
def ptd_logpdf(x, alpha, beta):
return ptd_weibull.logpdf(x, alpha, beta)
@pytensor_jit
def ptd_entropy(alpha, beta):
return ptd_weibull.entropy(alpha, beta)
@pytensor_jit
def ptd_mean(alpha, beta):
return ptd_weibull.mean(alpha, beta)
@pytensor_jit
def ptd_mode(alpha, beta):
return ptd_weibull.mode(alpha, beta)
@pytensor_jit
def ptd_median(alpha, beta):
return ptd_weibull.median(alpha, beta)
@pytensor_jit
def ptd_var(alpha, beta):
return ptd_weibull.var(alpha, beta)
@pytensor_jit
def ptd_std(alpha, beta):
return ptd_weibull.std(alpha, beta)
@pytensor_jit
def ptd_skewness(alpha, beta):
return ptd_weibull.skewness(alpha, beta)
@pytensor_jit
def ptd_kurtosis(alpha, beta):
return ptd_weibull.kurtosis(alpha, beta)
@pytensor_jit
def ptd_lmoment1(alpha, beta):
return ptd_weibull.lmoment1(alpha, beta)
@pytensor_jit
def ptd_lmoment2(alpha, beta):
return ptd_weibull.lmoment2(alpha, beta)
@pytensor_jit
def ptd_lmoment3(alpha, beta):
return ptd_weibull.lmoment3(alpha, beta)
@pytensor_jit
def ptd_lmoment4(alpha, beta):
return ptd_weibull.lmoment4(alpha, beta)
@pytensor_rng_jit
def ptd_rvs(alpha, beta, size, rng):
return ptd_weibull.rvs(alpha, beta, size=size, random_state=rng)
