"""Created on Aug 03 21:35:28 2024"""
from typing import Dict
import numpy as np
from .backend import BaseDistribution
from .backend.errorHandling import NegativeAmplitudeError, NegativeScaleError, NegativeShapeError
from .utilities_d import skew_normal_cdf_, skew_normal_pdf_
[docs]
class SkewNormalDistribution(BaseDistribution):
r"""
Class for SkewNormal distribution.
:param amplitude: The amplitude of the PDF. Defaults to 1.0. Ignored if **normalize** is ``True``.
:type amplitude: float, optional
:param shape: The mean parameter, :math:`\mu`. Defaults to 0.0.
:type shape: float, optional
:param scale: The scale parameter, for scaling. Defaults to 1.0,
:type scale: float, optional
:param location: The location parameter, for shifting. Defaults to 0.0.
:type location: 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 NegativeStandardDeviationError: If the provided value of standard deviation is negative.
Examples
--------
Importing libraries:
.. literalinclude:: ../../../examples/basic/skewnormal.py
:language: python
:linenos:
:lineno-start: 3
:lines: 3-7
Generating a standard Skew Normal(:math:`\xi=1, \mu = 0, \sigma = 1`) distribution with ``pyMultiFit`` and ``scipy``:
.. literalinclude:: ../../../examples/basic/skewnormal.py
:language: python
:linenos:
:lineno-start: 9
:lines: 9-12
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/skewnormal.py
:language: python
:linenos:
:lineno-start: 14
:lines: 14-29
.. image:: ../../../images/skew_norm_example1.png
:alt: SkewNormal(1, 0, 1)
:align: center
Generating a translated Skew Normal(:math:`\xi=3, \mu=-3, \sigma=3`) distribution:
.. literalinclude:: ../../../examples/basic/skewnormal.py
:language: python
:lineno-start: 32
:lines: 32
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/skewnormal.py
:language: python
:lineno-start: 34
:lines: 34-49
.. image:: ../../../images/skew_norm_example2.png
:alt: Skew Normal(3, -3, 3)
:align: center
"""
def __init__(self, amplitude: float = 1.0, shape: float = 1., location: float = 0., scale: float = 1., normalize: bool = False):
if not normalize and amplitude < 0.:
raise NegativeAmplitudeError()
if scale <= 0.:
raise NegativeScaleError()
if shape <= 0.:
raise NegativeShapeError()
self.amplitude = 1 if normalize else amplitude
self.shape = shape
self.location = location
self.scale = scale
self.norm = normalize
[docs]
@classmethod
def scipy_like(cls, a: float, loc: float = 0.0, scale: float = 1.0):
"""
Instantiate SkewNormalDistribution with scipy parametrization.
Parameters
----------
a : float
The skewness parameter.
loc : float, optional
The location parameter. Defaults to 0.0.
scale : float, optional
The scale parameter. Defaults to 1.0.
Returns
-------
SkewNormalDistribution
An instance of normalized SkewNormalDistribution.
"""
return cls(shape=a, location=loc, scale=scale, normalize=True)
[docs]
def pdf(self, x: np.ndarray) -> np.ndarray:
return skew_normal_pdf_(x=x, amplitude=self.amplitude, shape=self.shape, loc=self.location, scale=self.scale, normalize=self.norm)
[docs]
def cdf(self, x: np.ndarray) -> np.ndarray:
return skew_normal_cdf_(x=x, amplitude=self.amplitude, shape=self.shape, loc=self.location, scale=self.scale, normalize=self.norm)
[docs]
def stats(self) -> Dict[str, float]:
alpha, omega, epsilon = self.shape, self.scale, self.location
delta = alpha / np.sqrt(1 + alpha**2)
def _m0(alpha_):
m0 = np.sqrt(2 / np.pi) * delta
m0 -= ((1 - np.pi / 4) * (np.sqrt(2 / np.pi) * delta)**3) / (1 - (2 / np.pi) * delta**2)
m0 -= (2 * np.pi / abs(alpha_)) * np.exp(-(2 * np.pi / abs(alpha_))) * np.sign(alpha_)
return m0
mean_ = epsilon + omega * delta * np.sqrt(2 / np.pi)
mode_ = epsilon + omega * _m0(alpha)
variance_ = omega**2 * (1 - (2 * delta**2 / np.pi))
return {'mean': mean_,
'mode': mode_,
'median': None,
'variance': variance_,
'std': np.sqrt(variance_)}