import numpy as np
from pytensor_distributions import kumaraswamy as ptd_kumaraswamy
from preliz.distributions.distributions import Continuous
from preliz.internal.distribution_helper import eps, pytensor_jit, pytensor_rng_jit
from preliz.internal.optimization import optimize_mean_sigma, optimize_ml
[docs]
class Kumaraswamy(Continuous):
r"""
Kumaraswamy distribution.
The pdf of this distribution is
.. math::
f(x \mid a, b) = a b x^{a - 1} (1 - x^a)^{b - 1}
.. plot::
:context: close-figs
from preliz import Kumaraswamy, style
style.use('preliz-doc')
a_s = [.5, 5., 1., 2., 2.]
b_s = [.5, 1., 3., 2., 5.]
for a, b in zip(a_s, b_s):
ax = Kumaraswamy(a, b).plot_pdf()
ax.set_ylim(0, 3.)
======== ==============================================================
Support :math:`x \in (0, 1)`
Mean :math:`b B(1 + \tfrac{1}{a}, b)`
Variance :math:`b B(1 + \tfrac{2}{a}, b) - (b B(1 + \tfrac{1}{a}, b))^2`
======== ==============================================================
Parameters
----------
a : float
a > 0.
b : float
b > 0.
"""
def __init__(self, a=None, b=None):
super().__init__()
self.support = (0, 1)
self._parametrization(a, b)
def _parametrization(self, a=None, b=None):
self.a = a
self.b = b
self.params = (self.a, self.b)
self.param_names = ("a", "b")
self.params_support = ((eps, np.inf), (eps, np.inf))
if (a and b) is not None:
self._update(a, b)
def _update(self, a, b):
self.a = np.float64(a)
self.b = np.float64(b)
self.params = (self.a, self.b)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.a, self.b)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.a, self.b)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.a, self.b)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.a, self.b)
[docs]
def entropy(self):
return ptd_entropy(self.a, self.b)
[docs]
def mean(self):
return ptd_mean(self.a, self.b)
[docs]
def mode(self):
return ptd_mode(self.a, self.b)
[docs]
def var(self):
return ptd_var(self.a, self.b)
[docs]
def std(self):
return ptd_std(self.a, self.b)
[docs]
def skewness(self):
return ptd_skewness(self.a, self.b)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.a, self.b)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.a, self.b)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.a, self.b)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.a, self.b)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.a, self.b)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.a, self.b, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
optimize_mean_sigma(self, mean, sigma)
def _fit_mle(self, sample, **kwargs):
optimize_ml(self, sample, **kwargs)
@pytensor_jit
def ptd_pdf(x, a, b):
return ptd_kumaraswamy.pdf(x, a, b)
@pytensor_jit
def ptd_cdf(x, a, b):
return ptd_kumaraswamy.cdf(x, a, b)
@pytensor_jit
def ptd_ppf(q, a, b):
return ptd_kumaraswamy.ppf(q, a, b)
@pytensor_jit
def ptd_logpdf(x, a, b):
return ptd_kumaraswamy.logpdf(x, a, b)
@pytensor_jit
def ptd_entropy(a, b):
return ptd_kumaraswamy.entropy(a, b)
@pytensor_jit
def ptd_mean(a, b):
return ptd_kumaraswamy.mean(a, b)
@pytensor_jit
def ptd_mode(a, b):
return ptd_kumaraswamy.mode(a, b)
@pytensor_jit
def ptd_median(a, b):
return ptd_kumaraswamy.median(a, b)
@pytensor_jit
def ptd_var(a, b):
return ptd_kumaraswamy.var(a, b)
@pytensor_jit
def ptd_std(a, b):
return ptd_kumaraswamy.std(a, b)
@pytensor_jit
def ptd_skewness(a, b):
return ptd_kumaraswamy.skewness(a, b)
@pytensor_jit
def ptd_kurtosis(a, b):
return ptd_kumaraswamy.kurtosis(a, b)
@pytensor_jit
def ptd_lmoment1(a, b):
return ptd_kumaraswamy.lmoment1(a, b)
@pytensor_jit
def ptd_lmoment2(a, b):
return ptd_kumaraswamy.lmoment2(a, b)
@pytensor_jit
def ptd_lmoment3(a, b):
return ptd_kumaraswamy.lmoment3(a, b)
@pytensor_jit
def ptd_lmoment4(a, b):
return ptd_kumaraswamy.lmoment4(a, b)
@pytensor_rng_jit
def ptd_rvs(a, b, size, rng):
return ptd_kumaraswamy.rvs(a, b, size=size, random_state=rng)
