"""BetaScaled distribution."""
import numpy as np
import pytensor.tensor as pt
from pytensor_distributions import betascaled as ptd_betascaled
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 BetaScaled(Continuous):
r"""
Scaled Beta distribution.
The pdf of this distribution is
.. math::
f(x \mid \alpha, \beta) =
\frac{(x-\text{lower})^{\alpha - 1} (\text{upper} - x)^{\beta - 1}}
{(\text{upper}-\text{lower})^{\alpha+\beta-1} B(\alpha, \beta)}
.. plot::
:context: close-figs
from preliz import BetaScaled, style
style.use('preliz-doc')
alphas = [2, 2]
betas = [2, 5]
lowers = [-0.5, -1]
uppers = [1.5, 2]
for alpha, beta, lower, upper in zip(alphas, betas, lowers, uppers):
BetaScaled(alpha, beta, lower, upper).plot_pdf()
======== ==============================================================
Support :math:`x \in (lower, upper)`
Mean :math:`\dfrac{\alpha}{\alpha + \beta} (upper-lower) + lower`
Variance :math:`\dfrac{\alpha \beta}{(\alpha+\beta)^2(\alpha+\beta+1)} (upper-lower)`
======== ==============================================================
Parameters
----------
alpha : float
alpha > 0
beta : float
beta > 0
lower: float
Lower limit.
upper: float
Upper limit (upper > lower).
"""
def __init__(self, alpha=None, beta=None, lower=0, upper=1):
super().__init__()
self.alpha = alpha
self.beta = beta
self.lower = lower
self.upper = upper
self.support = (lower, upper)
self._parametrization(self.alpha, self.beta, self.lower, self.upper)
def _parametrization(self, alpha=None, beta=None, lower=None, upper=None):
self.param_names = ("alpha", "beta", "lower", "upper")
self.params_support = ((eps, pt.inf), (eps, pt.inf), (-pt.inf, pt.inf), (-pt.inf, pt.inf))
if all_not_none(alpha, beta):
self._update(alpha, beta, lower, upper)
def _update(self, alpha, beta, lower=None, upper=None):
if lower is not None:
self.lower = np.float64(lower)
if upper is not None:
self.upper = np.float64(upper)
self.alpha = np.float64(alpha)
self.beta = np.float64(beta)
self.params = (self.alpha, self.beta, self.lower, self.upper)
self.support = self.lower, self.upper
self.is_frozen = True
def _from_mu_sigma(self, mu, sigma):
nu = mu * (1 - mu) / sigma**2 - 1
alpha = mu * nu
beta = (1 - mu) * nu
return alpha, beta
def _from_mu_nu(self, mu, nu):
alpha = mu * nu
beta = (1 - mu) * nu
return alpha, beta
def _to_mu_sigma(self, alpha, beta):
alpha_plus_beta = alpha + beta
mu = alpha / alpha_plus_beta
sigma = (alpha * beta) ** 0.5 / alpha_plus_beta / (alpha_plus_beta + 1) ** 0.5
return mu, sigma
def _fit_moments(self, mean, sigma):
mean = (mean - self.lower) / (self.upper - self.lower)
sigma = sigma / (self.upper - self.lower)
kappa = mean * (1 - mean) / sigma**2 - 1
alpha = max(0.5, kappa * mean)
beta = max(0.5, kappa * (1 - mean))
self._update(alpha, beta)
def _fit_mle(self, sample):
self._update(None, None, np.min(sample), np.max(sample))
optimize_ml(self, sample)
[docs]
def pdf(self, x):
return ptd_pdf(x, self.alpha, self.beta, self.lower, self.upper)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.alpha, self.beta, self.lower, self.upper)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.alpha, self.beta, self.lower, self.upper)
[docs]
def sf(self, x):
return ptd_sf(x, self.alpha, self.beta, self.lower, self.upper)
[docs]
def isf(self, q):
return ptd_isf(q, self.alpha, self.beta, self.lower, self.upper)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.alpha, self.beta, self.lower, self.upper)
[docs]
def logcdf(self, x):
return ptd_logcdf(x, self.alpha, self.beta, self.lower, self.upper)
[docs]
def logsf(self, x):
return ptd_logsf(x, self.alpha, self.beta, self.lower, self.upper)
def logisf(self, q):
return ptd_logisf(q, self.alpha, self.beta, self.lower, self.upper)
[docs]
def entropy(self):
return ptd_entropy(self.alpha, self.beta, self.lower, self.upper)
[docs]
def mean(self):
return ptd_mean(self.alpha, self.beta, self.lower, self.upper)
[docs]
def mode(self):
return ptd_mode(self.alpha, self.beta, self.lower, self.upper)
[docs]
def var(self):
return ptd_var(self.alpha, self.beta, self.lower, self.upper)
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def std(self):
return ptd_std(self.alpha, self.beta, self.lower, self.upper)
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def skewness(self):
return ptd_skewness(self.alpha, self.beta, self.lower, self.upper)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.alpha, self.beta, self.lower, self.upper)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.alpha, self.beta, self.lower, self.upper)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.alpha, self.beta, self.lower, self.upper)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.alpha, self.beta, self.lower, self.upper)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.alpha, self.beta, self.lower, self.upper)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.alpha, self.beta, self.lower, self.upper, size=size, rng=random_state)
@pytensor_jit
def ptd_pdf(x, alpha, beta, lower, upper):
return ptd_betascaled.pdf(x, alpha, beta, lower, upper)
@pytensor_jit
def ptd_cdf(x, alpha, beta, lower, upper):
return ptd_betascaled.cdf(x, alpha, beta, lower, upper)
@pytensor_jit
def ptd_ppf(q, alpha, beta, lower, upper):
return ptd_betascaled.ppf(q, alpha, beta, lower, upper)
@pytensor_jit
def ptd_sf(x, alpha, beta, lower, upper):
return ptd_betascaled.sf(x, alpha, beta, lower, upper)
@pytensor_jit
def ptd_isf(q, alpha, beta, lower, upper):
return ptd_betascaled.isf(q, alpha, beta, lower, upper)
@pytensor_jit
def ptd_logpdf(x, alpha, beta, lower, upper):
return ptd_betascaled.logpdf(x, alpha, beta, lower, upper)
@pytensor_jit
def ptd_logcdf(x, alpha, beta, lower, upper):
return ptd_betascaled.logcdf(x, alpha, beta, lower, upper)
@pytensor_jit
def ptd_logsf(x, alpha, beta, lower, upper):
return ptd_betascaled.logsf(x, alpha, beta, lower, upper)
@pytensor_jit
def ptd_logisf(q, alpha, beta, lower, upper):
return ptd_betascaled.logisf(q, alpha, beta, lower, upper)
@pytensor_jit
def ptd_entropy(alpha, beta, lower, upper):
return ptd_betascaled.entropy(alpha, beta, lower, upper)
@pytensor_jit
def ptd_mean(alpha, beta, lower, upper):
return ptd_betascaled.mean(alpha, beta, lower, upper)
@pytensor_jit
def ptd_mode(alpha, beta, lower, upper):
return ptd_betascaled.mode(alpha, beta, lower, upper)
@pytensor_jit
def ptd_median(alpha, beta, lower, upper):
return ptd_betascaled.median(alpha, beta, lower, upper)
@pytensor_jit
def ptd_var(alpha, beta, lower, upper):
return ptd_betascaled.var(alpha, beta, lower, upper)
@pytensor_jit
def ptd_std(alpha, beta, lower, upper):
return ptd_betascaled.std(alpha, beta, lower, upper)
@pytensor_jit
def ptd_skewness(alpha, beta, lower, upper):
return ptd_betascaled.skewness(alpha, beta, lower, upper)
@pytensor_jit
def ptd_kurtosis(alpha, beta, lower, upper):
return ptd_betascaled.kurtosis(alpha, beta, lower, upper)
@pytensor_jit
def ptd_lmoment1(alpha, beta, lower, upper):
return ptd_betascaled.lmoment1(alpha, beta, lower, upper)
@pytensor_jit
def ptd_lmoment2(alpha, beta, lower, upper):
return ptd_betascaled.lmoment2(alpha, beta, lower, upper)
@pytensor_jit
def ptd_lmoment3(alpha, beta, lower, upper):
return ptd_betascaled.lmoment3(alpha, beta, lower, upper)
@pytensor_jit
def ptd_lmoment4(alpha, beta, lower, upper):
return ptd_betascaled.lmoment4(alpha, beta, lower, upper)
@pytensor_rng_jit
def ptd_rvs(alpha, beta, lower, upper, size, rng):
return ptd_betascaled.rvs(alpha, beta, lower, upper, size=size, random_state=rng)
