"""Created on Jan 29 15:42:23 2025"""
from typing import Dict
import numpy as np
from scipy.special import gammaln
from ..backend import BaseDistribution, errorHandling as erH
from ..utilities_d import sym_gen_normal_pdf_, sym_gen_normal_cdf_
from ... import md_scipy_like
[docs]
class SymmetricGeneralizedNormalDistribution(BaseDistribution):
r"""
Class for SymmetricGeneralizedNormalDistribution.
:param amplitude: The amplitude of the PDF. Defaults to 1.0. Ignored if **normalize** is ``True``.
:type amplitude: float, optional
:param shape: The shape parameter, :math:`\beta`. Defaults to 1.0.
:type shape: float, optional
:param loc: The shape parameter, :math:`\mu`. Defaults to 0.0.
:type loc: float, optional
:param scale: The standard deviation parameter, :math:`\alpha`. Defaults to 1.0.
:type scale: 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 NegativeScaleError: If the provided value of scale parameter is negative.
Examples
--------
Importing libraries:
.. literalinclude:: ../../../examples/basic/gaussian.py
:language: python
:linenos:
:lineno-start: 3
:lines: 3-7
Generating a standard SymmetricGeneralizedNormalDistribution(:math:`\beta=1, \mu=0, \alpha = 1`)
with ``pyMultiFit`` and ``scipy``:
.. literalinclude:: ../../../examples/basic/gennorm.py
:language: python
:linenos:
:lineno-start: 9
:lines: 9-12
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/gennorm.py
:language: python
:linenos:
:lineno-start: 14
:lines: 14-29
.. image:: ../../../images/gen_norm_example1.png
:alt: GenNorm(1, 0, 1)
:align: center
Generating a scaled and translated SymmetricGeneralizedNormalDistribution(:math:`\beta=2, \mu=-3, \alpha=5`):
.. literalinclude:: ../../../examples/basic/gennorm.py
:language: python
:lineno-start: 32
:lines: 32
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/gennorm.py
:language: python
:lineno-start: 34
:lines: 34-49
.. image:: ../../../images/gen_norm_example2.png
:alt: GenNorm(2, -3, 5)
:align: center
"""
def __init__(
self, amplitude: float = 1.0, shape: float = 1.0, loc: float = 0.0, scale: float = 1.0, normalize: bool = False
):
if amplitude < 0 and not normalize:
raise erH.NegativeAmplitudeError()
if shape < 0:
raise erH.NegativeShapeError()
self.amplitude = 1.0 if normalize else amplitude
self.loc = loc
self.scale = scale
self.shape = shape
self.norm = normalize
[docs]
@classmethod
@md_scipy_like("1.0.7")
def scipy_like(cls, beta, loc: float = 0.0, scale: float = 1.0):
"""
Instantiate SymmetricGeneralizedNormalDistribution with scipy parametrization.
Parameters
----------
beta: float
The shape parameter.
loc: float, optional
The mean parameter. Defaults to 0.0.
scale: float, optional
The scale parameter. Defaults to 1.0.
Returns
-------
SymmetricGeneralizedNormalDistribution
An instance of normalized SymmetricGeneralizedNormalDistribution.
"""
return cls(shape=beta, loc=loc, scale=scale, normalize=True)
[docs]
@classmethod
def from_scipy_params(cls, beta, loc: float = 0.0, scale: float = 1.0):
"""
Instantiate SymmetricGeneralizedNormalDistribution with scipy parametrization.
Parameters
----------
beta: float
The shape parameter.
loc: float, optional
The mean parameter. Defaults to 0.0.
scale: float, optional
The scale parameter. Defaults to 1.0.
Returns
-------
SymmetricGeneralizedNormalDistribution
An instance of normalized SymmetricGeneralizedNormalDistribution.
"""
return cls(shape=beta, loc=loc, scale=scale, normalize=True)
[docs]
def pdf(self, x: np.ndarray) -> np.ndarray:
return sym_gen_normal_pdf_(
x, amplitude=self.amplitude, shape=self.shape, loc=self.loc, scale=self.scale, normalize=self.norm
)
[docs]
def cdf(self, x: np.ndarray) -> np.ndarray:
return sym_gen_normal_cdf_(
x, amplitude=self.amplitude, shape=self.shape, loc=self.loc, scale=self.scale, normalize=self.norm
)
[docs]
def stats(self) -> Dict[str, float]:
mean_ = self.loc
median_ = self.loc
mode_ = self.loc
variance_ = 2 * np.log(self.scale) + gammaln(3 / self.shape) - gammaln(1 / self.shape)
variance_ = np.exp(variance_)
return {"mean": mean_, "median": median_, "mode": mode_, "variance": variance_, "std": np.sqrt(variance_)}