"""Created on Aug 14 00:45:37 2024"""
from typing import Dict
import numpy as np
from scipy.special import betaincinv
from .backend import BaseDistribution, errorHandling as erH
from .utilities_d import beta_cdf_, beta_pdf_, beta_log_pdf_, beta_log_cdf_
from .. import md_scipy_like
[docs]
class BetaDistribution(BaseDistribution):
r"""
Class for Beta distribution.
:param amplitude: The amplitude of the PDF. Defaults to 1.0. Ignored if ``normalize`` is ``True``.
:type amplitude: float, optional
:param alpha: The :math:`\alpha` parameter. Defaults to 1.0.
:type alpha: float, optional
:param beta: The :math:`\beta` parameter. Defaults to 1.0.
:type beta: float, optional
:param loc: float, optional The location parameter, for shifting. Defaults to 0.0.
:type loc: float, optional
:param scale: float, optional The scale parameter, for scaling. Defaults to 1.0.
:type scale: float, optional
:param normalize: bool, optional If ``True``, the distribution is normalized so that the total area under the PDF equals 1. Defaults to ``False``.
:type normalize: bool, optional
:raise NegativeAmplitudeError: If the provided value of amplitude is negative.
:raise NegativeAlphaError: If the provided value of :math:`\alpha` is negative.
:raise NegativeBetaError: If the provided value of :math:`\beta` is negative.
Examples
--------
Importing libraries
.. literalinclude:: ../../../examples/basic/beta1.py
:language: python
:linenos:
:lineno-start: 3
:lines: 3-7
Generating a standard :math:`\text{Beta}(2, 30)` distribution with ``pyMultiFit`` and ``scipy``.
.. literalinclude:: ../../../examples/basic/beta1.py
:language: python
:linenos:
:lineno-start: 9
:lines: 9-12
Plotting **PDF** and **CDF**
.. literalinclude:: ../../../examples/basic/beta1.py
:language: python
:linenos:
:lineno-start: 14
:lines: 14-29
.. image:: ../../../images/beta_example1.png
:alt: Beta distribution (5, 30)
:align: center
Generating a shifted and translated :math:`\text{Beta}(2, 30)` distribution.
.. literalinclude:: ../../../examples/basic/beta2.py
:language: python
:lineno-start: 9
:lines: 9-12
Plotting **PDF** and **CDF**
.. literalinclude:: ../../../examples/basic/beta2.py
:language: python
:lineno-start: 14
:lines: 14-29
.. image:: ../../../images/beta_example2.png
:alt: Beta distribution (shifted and translated)
:align: center
"""
def __init__(
self,
amplitude: float = 1.0,
alpha: float = 1.0,
beta: float = 1.0,
loc: float = 0.0,
scale: float = 1.0,
normalize: bool = False,
):
if not normalize and amplitude <= 0:
raise erH.NegativeAmplitudeError()
if alpha <= 0:
raise erH.NegativeAlphaError()
if beta <= 0:
raise erH.NegativeBetaError()
self.amplitude = 1.0 if normalize else amplitude
self.alpha = alpha
self.beta = beta
self.loc = loc
self.scale = scale
self.norm = normalize
[docs]
@classmethod
@md_scipy_like('v1.0.7')
def scipy_like(cls, a: float, b: float, loc: float = 0.0, scale: float = 1.0) -> 'BetaDistribution':
r"""
Instantiate BetaDistribution with scipy parameterization.
Parameters
----------
a: float
The shape parameter, :math:`\alpha`.
b: float
The shape parameter, :math:`\beta`.
loc: float, optional
The location parameter. Defaults to 0.0.
scale: float, optional
The scale parameter,. Defaults to 1.0.
Returns
-------
BetaDistribution
An instance of normalized BetaDistribution.
"""
return cls(alpha=a, beta=b, loc=loc, scale=scale, normalize=True)
[docs]
@classmethod
def from_scipy_params(cls, a: float, b: float, loc: float = 0.0, scale: float = 1.0) -> 'BetaDistribution':
r"""
Instantiate BetaDistribution with scipy parameterization.
Parameters
----------
a: float
The shape parameter, :math:`\alpha`.
b: float
The shape parameter, :math:`\beta`.
loc: float, optional
The location parameter. Defaults to 0.0.
scale: float, optional
The scale parameter,. Defaults to 1.0.
Returns
-------
BetaDistribution
An instance of normalized BetaDistribution.
"""
return cls(alpha=a, beta=b, loc=loc, scale=scale, normalize=True)
[docs]
def pdf(self, x: np.ndarray) -> np.ndarray:
return beta_pdf_(
x,
amplitude=self.amplitude,
alpha=self.alpha,
beta_=self.beta,
loc=self.loc,
scale=self.scale,
normalize=self.norm,
)
[docs]
def logpdf(self, x: np.ndarray) -> np.ndarray:
return beta_log_pdf_(
x,
amplitude=self.amplitude,
alpha=self.alpha,
beta_=self.beta,
loc=self.loc,
scale=self.scale,
normalize=self.norm,
)
[docs]
def cdf(self, x: np.ndarray) -> np.ndarray:
return beta_cdf_(
x,
amplitude=self.amplitude,
alpha=self.alpha,
beta_=self.beta,
loc=self.loc,
scale=self.scale,
normalize=self.norm,
)
[docs]
def logcdf(self, x: np.ndarray) -> np.ndarray:
return beta_log_cdf_(
x,
amplitude=self.amplitude,
alpha=self.alpha,
beta_=self.beta,
loc=self.loc,
scale=self.scale,
normalize=self.norm,
)
[docs]
def stats(self) -> Dict[str, float]:
a, b = self.alpha, self.beta
s, _l = self.scale, self.loc
mean_ = a / (a + b)
mean_ = (s * mean_) + _l
median_ = betaincinv(a, b, 0.5)
median_ = (s * median_) + _l
num_ = a * b
den_ = (a + b)**2 * (a + b + 1)
variance_ = s**2 * (num_ / den_)
return {
"mean": mean_,
"median": median_.astype(float),
"variance": variance_,
"std": np.sqrt(variance_),
}