import numpy as np
import pytensor.tensor as pt
from pytensor_distributions import asymmetriclaplace as ptd_asymmetriclaplace
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 AsymmetricLaplace(Continuous):
r"""
Asymmetric-Laplace distribution.
The pdf of this distribution is
.. math::
{f(x|\\b,\kappa,\mu) =
\left({\frac{\\b}{\kappa + 1/\kappa}}\right)\,e^{-(x-\mu)\\b\,s\kappa ^{s}}}
where
.. math::
s = sgn(x-\mu)
.. plot::
:context: close-figs
from preliz import AsymmetricLaplace, style
style.use('preliz-doc')
kappas = [1., 2., .5]
mus = [0., 0., 3.]
bs = [1., 1., 1.]
for kappa, mu, b in zip(kappas, mus, bs):
AsymmetricLaplace(kappa, mu, b).plot_pdf(support=(-10,10))
======== ========================
Support :math:`x \in \mathbb{R}`
Mean :math:`\mu-\frac{\\\kappa-1/\kappa}b`
Variance :math:`\frac{1+\kappa^{4}}{b^2\kappa^2 }`
======== ========================
AsymmetricLaplace distribution has 2 alternative parametrizations. In terms of kappa,
mu and b or q, mu and b.
The link between the 2 alternatives is given by
.. math::
\kappa = \sqrt(\frac{q}{1-q})
Parameters
----------
kappa : float
Symmetry parameter (kappa > 0).
mu : float
Location parameter.
b : float
Scale parameter (b > 0).
q : float
Symmetry parameter (0 < q < 1).
"""
def __init__(self, kappa=None, mu=None, b=None, q=None):
super().__init__()
self.support = (-pt.inf, pt.inf)
self._parametrization(kappa, mu, b, q)
def _parametrization(self, kappa=None, mu=None, b=None, q=None):
if all_not_none(kappa, q):
raise ValueError("Incompatible parametrization. Either use kappa or q.")
self.param_names = ("kappa", "mu", "b")
self.params_support = ((eps, pt.inf), (-pt.inf, pt.inf), (eps, pt.inf))
if q is not None:
self.q = q
kappa = _from_q(q)
self.param_names = ("q", "mu", "b")
self.params_support = ((eps, 1 - eps), (-pt.inf, pt.inf), (eps, pt.inf))
self.kappa = kappa
self.mu = mu
self.b = b
if all_not_none(kappa, mu, b):
self._update(kappa, mu, b)
def _update(self, kappa, mu, b):
self.kappa = np.float64(kappa)
self.mu = np.float64(mu)
self.b = np.float64(b)
self.q = _to_q(self.kappa)
if self.param_names[0] == "kappa":
self.params = (self.kappa, self.mu, self.b)
elif self.param_names[0] == "q":
self.params = (self.q, self.mu, self.b)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.mu, self.b, self.kappa)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.mu, self.b, self.kappa)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.mu, self.b, self.kappa)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.mu, self.b, self.kappa)
[docs]
def entropy(self):
return ptd_entropy(self.mu, self.b, self.kappa)
[docs]
def mean(self):
return ptd_mean(self.mu, self.b, self.kappa)
[docs]
def mode(self):
return ptd_mode(self.mu, self.b, self.kappa)
[docs]
def var(self):
return ptd_var(self.mu, self.b, self.kappa)
[docs]
def std(self):
return ptd_std(self.mu, self.b, self.kappa)
[docs]
def skewness(self):
return ptd_skewness(self.mu, self.b, self.kappa)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.mu, self.b, self.kappa)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.mu, self.b, self.kappa)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.mu, self.b, self.kappa)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.mu, self.b, self.kappa)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.mu, self.b, self.kappa)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.mu, self.b, self.kappa, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
# Assume symmetry
mu = mean
b = (sigma / 2) * (2**0.5)
self._update(1, mu, b)
def _fit_mle(self, sample):
optimize_ml(self, sample)
@pytensor_jit
def ptd_pdf(x, mu, b, kappa):
return ptd_asymmetriclaplace.pdf(x, mu, b, kappa)
@pytensor_jit
def ptd_cdf(x, mu, b, kappa):
return ptd_asymmetriclaplace.cdf(x, mu, b, kappa)
@pytensor_jit
def ptd_ppf(q, mu, b, kappa):
return ptd_asymmetriclaplace.ppf(q, mu, b, kappa)
@pytensor_jit
def ptd_logpdf(x, mu, b, kappa):
return ptd_asymmetriclaplace.logpdf(x, mu, b, kappa)
@pytensor_jit
def ptd_entropy(mu, b, kappa):
return ptd_asymmetriclaplace.entropy(mu, b, kappa)
@pytensor_jit
def ptd_mean(mu, b, kappa):
return ptd_asymmetriclaplace.mean(mu, b, kappa)
@pytensor_jit
def ptd_mode(mu, b, kappa):
return ptd_asymmetriclaplace.mode(mu, b, kappa)
@pytensor_jit
def ptd_median(mu, b, kappa):
return ptd_asymmetriclaplace.median(mu, b, kappa)
@pytensor_jit
def ptd_var(mu, b, kappa):
return ptd_asymmetriclaplace.var(mu, b, kappa)
@pytensor_jit
def ptd_std(mu, b, kappa):
return ptd_asymmetriclaplace.std(mu, b, kappa)
@pytensor_jit
def ptd_skewness(mu, b, kappa):
return ptd_asymmetriclaplace.skewness(mu, b, kappa)
@pytensor_jit
def ptd_kurtosis(mu, b, kappa):
return ptd_asymmetriclaplace.kurtosis(mu, b, kappa)
@pytensor_jit
def ptd_lmoment1(mu, b, kappa):
return ptd_asymmetriclaplace.lmoment1(mu, b, kappa)
@pytensor_jit
def ptd_lmoment2(mu, b, kappa):
return ptd_asymmetriclaplace.lmoment2(mu, b, kappa)
@pytensor_jit
def ptd_lmoment3(mu, b, kappa):
return ptd_asymmetriclaplace.lmoment3(mu, b, kappa)
@pytensor_jit
def ptd_lmoment4(mu, b, kappa):
return ptd_asymmetriclaplace.lmoment4(mu, b, kappa)
@pytensor_rng_jit
def ptd_rvs(mu, b, kappa, size, rng):
return ptd_asymmetriclaplace.rvs(mu, b, kappa, size=size, random_state=rng)
def _from_q(q):
kappa = (q / (1 - q)) ** 0.5
return kappa
def _to_q(kappa):
q = kappa**2 / (1 + kappa**2)
return q
