"""Created on Aug 14 01:28:13 2024"""
from typing import Dict
import numpy as np
from .backend import BaseDistribution, errorHandling as erH
from .utilities_d import gamma_pdf_, gamma_log_pdf_, gamma_cdf_, gamma_log_cdf_
from .. import md_scipy_like, OneDArray
[docs]
class GammaDistribution(BaseDistribution):
r"""
Class for Gamma distribution with shape and scale parameters.
:param amplitude: The amplitude of the PDF. Default is 1.0. Ignored if **normalize** is ``True``.
:type amplitude: float, optional
:param shape: The shape parameter, :math:`\alpha`. Defaults to 1.0.
:type shape: float, optional
:param scale: The rate parameter, :math:`\theta`. Defaults to 1.0.
:type scale: float, optional
:param loc: The location parameter, for shifting. Defaults to 0.0.
:type loc: float, optional
:param normalize: 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 NegativeShapeError: If the provided value of shape is negative.
:raise NegativeScaleError: If the provided value of scale is negative.
Examples
--------
Importing libraries:
.. literalinclude:: ../../../examples/basic/gamma_.py
:language: python
:linenos:
:lineno-start: 3
:lines: 3-7
Generating a standard GammaSS(:math:`\alpha =1.5, \lambda = 1`) distribution with ``pyMultiFit`` and ``scipy``:
.. literalinclude:: ../../../examples/basic/gamma_.py
:language: python
:linenos:
:lineno-start: 9
:lines: 9-12
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/gamma_.py
:language: python
:linenos:
:lineno-start: 14
:lines: 14-29
.. image:: ../../../images/gammaSS_example1.png
:alt: GammaSS(1.5, 1)
:align: center
Generating a translated Gamma(:math:`\alpha=1.5, \lambda=0.2`) distribution with :math:`\text{loc} = 3`:
.. literalinclude:: ../../../examples/basic/gamma_.py
:language: python
:lineno-start: 32
:lines: 32
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/gamma_.py
:language: python
:lineno-start: 34
:lines: 34-49
.. image:: ../../../images/gammaSS_example2.png
:alt: GammaSS(1.5, 0.2, 3)
:align: center
"""
def __init__(
self, amplitude: float = 1.0, shape: float = 1.0, scale: float = 1.0, loc: float = 0.0, normalize: bool = False
):
if not normalize and amplitude <= 0:
raise erH.NegativeAmplitudeError()
if shape <= 0:
raise erH.NegativeShapeError()
if scale <= 0:
raise erH.NegativeScaleError()
self.amplitude = 1.0 if normalize else amplitude
self.shape = shape
self.scale = scale
self.loc = loc
self.norm = normalize
[docs]
@classmethod
@md_scipy_like("1.0.7")
def scipy_like(cls, a: float, loc: float = 0.0, scale: float = 1.0) -> "GammaDistribution":
r"""
Instantiate GammaDistributionSS with scipy parametrization.
Parameters
----------
a: float
The shape parameter.
loc: float, optional
The location parameter. Defaults to 0.0.
scale: float, optional
The scaling parameter. Defaults to 1.0.
Returns
-------
GammaDistribution
An instance of normalized GammaDistributionSS.
"""
return cls(shape=a, loc=loc, scale=scale, normalize=True)
[docs]
@classmethod
def from_scipy_params(cls, a: float, loc: float = 0.0, scale: float = 1.0) -> "GammaDistribution":
r"""
Instantiate GammaDistributionSS with scipy parametrization.
Parameters
----------
a: float
The shape parameter.
loc: float, optional
The location parameter. Defaults to 0.0.
scale: float, optional
The scaling parameter. Defaults to 1.0.
Returns
-------
GammaDistribution
An instance of normalized GammaDistributionSS.
"""
return cls(shape=a, loc=loc, scale=scale, normalize=True)
[docs]
def pdf(self, x: OneDArray) -> OneDArray:
return gamma_pdf_(
x, amplitude=self.amplitude, alpha=self.shape, theta=self.scale, loc=self.loc, normalize=self.norm
)
[docs]
def logpdf(self, x: OneDArray) -> OneDArray:
return gamma_log_pdf_(
x, amplitude=self.amplitude, alpha=self.shape, theta=self.scale, loc=self.loc, normalize=self.norm
)
[docs]
def cdf(self, x: OneDArray) -> OneDArray:
return gamma_cdf_(
x, amplitude=self.amplitude, alpha=self.shape, theta=self.scale, loc=self.loc, normalize=self.norm
)
[docs]
def logcdf(self, x: OneDArray) -> OneDArray:
return gamma_log_cdf_(
x, amplitude=self.amplitude, alpha=self.shape, theta=self.scale, loc=self.loc, normalize=self.norm
)
[docs]
def stats(self) -> Dict[str, float]:
s, r, l_ = self.shape, self.scale, self.loc
mean_ = (s * r) + l_
variance_ = s * r**2
mode_ = (s - 1) * r + l_ if s >= 1 else 0
return {"mean": mean_, "mode": mode_, "variance": variance_, "std": np.sqrt(variance_)}