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