import numpy as np
from pytensor_distributions import gumbel as ptd_gumbel
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
[docs]
class Gumbel(Continuous):
r"""
Gumbel distribution.
The pdf of this distribution is
.. math::
f(x \mid \mu, \beta) = \frac{1}{\beta}e^{-(z + e^{-z})}
where
.. math::
z = \frac{x - \mu}{\beta}
.. plot::
:context: close-figs
from preliz import Gumbel, style
style.use('preliz-doc')
mus = [0., 4., -1.]
betas = [1., 2., 4.]
for mu, beta in zip(mus, betas):
Gumbel(mu, beta).plot_pdf(support=(-10,20))
======== ==========================================
Support :math:`x \in \mathbb{R}`
Mean :math:`\mu + \beta\gamma`, where :math:`\gamma` is the Euler-Mascheroni constant
Variance :math:`\frac{\pi^2}{6} \beta^2`
======== ==========================================
Parameters
----------
mu : float
Location parameter.
beta : float
Scale parameter (beta > 0).
"""
def __init__(self, mu=None, beta=None):
super().__init__()
self.support = (-np.inf, np.inf)
self._parametrization(mu, beta)
def _parametrization(self, mu=None, beta=None):
self.mu = mu
self.beta = beta
self.params = (self.mu, self.beta)
self.param_names = ("mu", "beta")
self.params_support = ((-np.inf, np.inf), (eps, np.inf))
if all_not_none(self.mu, self.beta):
self._update(self.mu, self.beta)
def _update(self, mu, beta):
self.mu = np.float64(mu)
self.beta = np.float64(beta)
self.params = (self.mu, self.beta)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.mu, self.beta)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.mu, self.beta)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.mu, self.beta)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.mu, self.beta)
[docs]
def entropy(self):
return ptd_entropy(self.mu, self.beta)
[docs]
def mean(self):
return ptd_mean(self.mu, self.beta)
[docs]
def mode(self):
return ptd_mode(self.mu, self.beta)
[docs]
def var(self):
return ptd_var(self.mu, self.beta)
[docs]
def std(self):
return ptd_std(self.mu, self.beta)
[docs]
def skewness(self):
return ptd_skewness(self.mu, self.beta)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.mu, self.beta)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.mu, self.beta)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.mu, self.beta)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.mu, self.beta)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.mu, self.beta)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.mu, self.beta, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
beta = sigma / np.pi * 6**0.5
mu = mean - beta * np.euler_gamma
self._update(mu, beta)
def _fit_mle(self, sample):
optimize_ml(self, sample)
@pytensor_jit
def ptd_pdf(x, mu, beta):
return ptd_gumbel.pdf(x, mu, beta)
@pytensor_jit
def ptd_cdf(x, mu, beta):
return ptd_gumbel.cdf(x, mu, beta)
@pytensor_jit
def ptd_ppf(q, mu, beta):
return ptd_gumbel.ppf(q, mu, beta)
@pytensor_jit
def ptd_logpdf(x, mu, beta):
return ptd_gumbel.logpdf(x, mu, beta)
@pytensor_jit
def ptd_entropy(mu, beta):
return ptd_gumbel.entropy(mu, beta)
@pytensor_jit
def ptd_mean(mu, beta):
return ptd_gumbel.mean(mu, beta)
@pytensor_jit
def ptd_mode(mu, beta):
return ptd_gumbel.mode(mu, beta)
@pytensor_jit
def ptd_median(mu, beta):
return ptd_gumbel.median(mu, beta)
@pytensor_jit
def ptd_var(mu, beta):
return ptd_gumbel.var(mu, beta)
@pytensor_jit
def ptd_std(mu, beta):
return ptd_gumbel.std(mu, beta)
@pytensor_jit
def ptd_skewness(mu, beta):
return ptd_gumbel.skewness(mu, beta)
@pytensor_jit
def ptd_kurtosis(mu, beta):
return ptd_gumbel.kurtosis(mu, beta)
@pytensor_jit
def ptd_lmoment1(mu, beta):
return ptd_gumbel.lmoment1(mu, beta)
@pytensor_jit
def ptd_lmoment2(mu, beta):
return ptd_gumbel.lmoment2(mu, beta)
@pytensor_jit
def ptd_lmoment3(mu, beta):
return ptd_gumbel.lmoment3(mu, beta)
@pytensor_jit
def ptd_lmoment4(mu, beta):
return ptd_gumbel.lmoment4(mu, beta)
@pytensor_rng_jit
def ptd_rvs(mu, beta, size, rng):
return ptd_gumbel.rvs(mu, beta, size=size, random_state=rng)
