import numpy as np
from pytensor_distributions import logistic as ptd_logistic
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 Logistic(Continuous):
r"""
Logistic distribution.
The pdf of this distribution is
.. math::
f(x \mid \mu, s) =
\frac{ \exp ( - \frac{x - \mu}{s})}{s(1 + \exp ( - \frac{x - \mu}{s}))^2}
.. plot::
:context: close-figs
from preliz import Logistic, style
style.use('preliz-doc')
mus = [0., 0., -2.]
ss = [1., 2., .4]
for mu, s in zip(mus, ss):
Logistic(mu, s).plot_pdf(support=(-5,5))
========= ==========================================
Support :math:`x \in \mathbb{R}`
Mean :math:`\mu`
Variance :math:`\frac{s^2 \pi^2}{3}`
========= ==========================================
Parameters
----------
mu : float
Mean.
s : float
Scale (s > 0).
"""
def __init__(self, mu=None, s=None):
super().__init__()
self.support = (-np.inf, np.inf)
self._parametrization(mu, s)
def _parametrization(self, mu=None, s=None):
self.mu = mu
self.s = s
self.params = (self.mu, self.s)
self.param_names = ("mu", "s")
self.params_support = ((-np.inf, np.inf), (eps, np.inf))
if all_not_none(self.mu, self.s):
self._update(self.mu, self.s)
def _update(self, mu, s):
self.mu = np.float64(mu)
self.s = np.float64(s)
self.params = (self.mu, self.s)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.mu, self.s)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.mu, self.s)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.mu, self.s)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.mu, self.s)
[docs]
def entropy(self):
return ptd_entropy(self.mu, self.s)
[docs]
def mean(self):
return ptd_mean(self.mu, self.s)
[docs]
def mode(self):
return ptd_mode(self.mu, self.s)
[docs]
def var(self):
return ptd_var(self.mu, self.s)
[docs]
def std(self):
return ptd_std(self.mu, self.s)
[docs]
def skewness(self):
return ptd_skewness(self.mu, self.s)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.mu, self.s)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.mu, self.s)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.mu, self.s)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.mu, self.s)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.mu, self.s)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.mu, self.s, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
s = (3 * sigma**2 / np.pi**2) ** 0.5
self._update(mean, s)
def _fit_mle(self, sample):
optimize_ml(self, sample)
@pytensor_jit
def ptd_pdf(x, mu, s):
return ptd_logistic.pdf(x, mu, s)
@pytensor_jit
def ptd_cdf(x, mu, s):
return ptd_logistic.cdf(x, mu, s)
@pytensor_jit
def ptd_ppf(q, mu, s):
return ptd_logistic.ppf(q, mu, s)
@pytensor_jit
def ptd_logpdf(x, mu, s):
return ptd_logistic.logpdf(x, mu, s)
@pytensor_jit
def ptd_entropy(mu, s):
return ptd_logistic.entropy(mu, s)
@pytensor_jit
def ptd_mean(mu, s):
return ptd_logistic.mean(mu, s)
@pytensor_jit
def ptd_mode(mu, s):
return ptd_logistic.mode(mu, s)
@pytensor_jit
def ptd_median(mu, s):
return ptd_logistic.median(mu, s)
@pytensor_jit
def ptd_var(mu, s):
return ptd_logistic.var(mu, s)
@pytensor_jit
def ptd_std(mu, s):
return ptd_logistic.std(mu, s)
@pytensor_jit
def ptd_skewness(mu, s):
return ptd_logistic.skewness(mu, s)
@pytensor_jit
def ptd_kurtosis(mu, s):
return ptd_logistic.kurtosis(mu, s)
@pytensor_jit
def ptd_lmoment1(mu, s):
return ptd_logistic.lmoment1(mu, s)
@pytensor_jit
def ptd_lmoment2(mu, s):
return ptd_logistic.lmoment2(mu, s)
@pytensor_jit
def ptd_lmoment3(mu, s):
return ptd_logistic.lmoment3(mu, s)
@pytensor_jit
def ptd_lmoment4(mu, s):
return ptd_logistic.lmoment4(mu, s)
@pytensor_rng_jit
def ptd_rvs(mu, s, size, rng):
return ptd_logistic.rvs(mu, s, size=size, random_state=rng)
