import numba as nb
import numpy as np
from pytensor_distributions import laplace as ptd_laplace
from preliz.distributions.distributions import Continuous
from preliz.internal.distribution_helper import all_not_none, eps, pytensor_jit, pytensor_rng_jit
[docs]
class Laplace(Continuous):
r"""
Laplace distribution.
The pdf of this distribution is
.. math::
f(x \mid \mu, b) =
\frac{1}{2b} \exp \left\{ - \frac{|x - \mu|}{b} \right\}
.. plot::
:context: close-figs
from preliz import Laplace, style
style.use('preliz-doc')
mus = [0., 0., 0., -5.]
bs = [1., 2., 4., 4.]
for mu, b in zip(mus, bs):
Laplace(mu, b).plot_pdf(support=(-10,10))
======== ========================
Support :math:`x \in \mathbb{R}`
Mean :math:`\mu`
Variance :math:`2 b^2`
======== ========================
Parameters
----------
mu : float
Location parameter.
b : float
Scale parameter (b > 0).
"""
def __init__(self, mu=None, b=None):
super().__init__()
self.support = (-np.inf, np.inf)
self._parametrization(mu, b)
def _parametrization(self, mu=None, b=None):
self.mu = mu
self.b = b
self.params = (self.mu, self.b)
self.param_names = ("mu", "b")
self.params_support = ((-np.inf, np.inf), (eps, np.inf))
if all_not_none(mu, b):
self._update(mu, b)
def _update(self, mu, b):
self.mu = np.float64(mu)
self.b = np.float64(b)
self.params = (self.mu, self.b)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.mu, self.b)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.mu, self.b)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.mu, self.b)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.mu, self.b)
[docs]
def entropy(self):
return ptd_entropy(self.mu, self.b)
[docs]
def mean(self):
return ptd_mean(self.mu, self.b)
[docs]
def mode(self):
return ptd_mode(self.mu, self.b)
[docs]
def std(self):
return ptd_std(self.mu, self.b)
[docs]
def var(self):
return ptd_var(self.mu, self.b)
[docs]
def skewness(self):
return ptd_skewness(self.mu, self.b)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.mu, self.b)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.mu, self.b)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.mu, self.b)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.mu, self.b)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.mu, self.b)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.mu, self.b, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
b = (sigma / 2) * (2**0.5)
self._update(mean, b)
def _fit_mle(self, sample):
mu, b = nb_fit_mle(sample)
self._update(mu, b)
@pytensor_jit
def ptd_pdf(x, mu, b):
return ptd_laplace.pdf(x, mu, b)
@pytensor_jit
def ptd_cdf(x, mu, b):
return ptd_laplace.cdf(x, mu, b)
@pytensor_jit
def ptd_ppf(q, mu, b):
return ptd_laplace.ppf(q, mu, b)
@pytensor_jit
def ptd_logpdf(x, mu, b):
return ptd_laplace.logpdf(x, mu, b)
@pytensor_jit
def ptd_entropy(mu, b):
return ptd_laplace.entropy(mu, b)
@pytensor_jit
def ptd_mean(mu, b):
return ptd_laplace.mean(mu, b)
@pytensor_jit
def ptd_mode(mu, b):
return ptd_laplace.mode(mu, b)
@pytensor_jit
def ptd_median(mu, b):
return ptd_laplace.median(mu, b)
@pytensor_jit
def ptd_var(mu, b):
return ptd_laplace.var(mu, b)
@pytensor_jit
def ptd_std(mu, b):
return ptd_laplace.std(mu, b)
@pytensor_jit
def ptd_skewness(mu, b):
return ptd_laplace.skewness(mu, b)
@pytensor_jit
def ptd_kurtosis(mu, b):
return ptd_laplace.kurtosis(mu, b)
@pytensor_jit
def ptd_lmoment1(mu, b):
return ptd_laplace.lmoment1(mu, b)
@pytensor_jit
def ptd_lmoment2(mu, b):
return ptd_laplace.lmoment2(mu, b)
@pytensor_jit
def ptd_lmoment3(mu, b):
return ptd_laplace.lmoment3(mu, b)
@pytensor_jit
def ptd_lmoment4(mu, b):
return ptd_laplace.lmoment4(mu, b)
@pytensor_rng_jit
def ptd_rvs(mu, b, size, rng):
return ptd_laplace.rvs(mu, b, size=size, random_state=rng)
@nb.njit(cache=True)
def nb_fit_mle(sample):
median = np.median(sample)
scale = np.sum(np.abs(sample - median)) / len(sample)
return median, scale
