"""Created on Nov 30 10:49:49 2024"""
from typing import Dict
import numpy as np
from .backend import BaseDistribution, errorHandling as erH
from .utilities_d import exponential_cdf_, exponential_pdf_, exponential_log_pdf_, exponential_log_cdf_
from .. import md_scipy_like
[docs]
class ExponentialDistribution(BaseDistribution):
r"""
Class for Exponential distribution.
:param amplitude: The amplitude of the PDF. Defaults to 1.0. Ignored if **normalize** is ``True``.
:type amplitude: float, optional
:param scale: The scale parameter, :math:`\lambda`. 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 NegativeScaleError: If the provided value of scale is negative.
Examples
--------
Importing libraries:
.. literalinclude:: ../../../examples/basic/expon.py
:language: python
:linenos:
:lineno-start: 3
:lines: 3-7
Generating a standard Exponential(:math:`\lambda =1.5`) distribution with ``pyMultiFit`` and ``scipy``:
.. literalinclude:: ../../../examples/basic/expon.py
:language: python
:linenos:
:lineno-start: 9
:lines: 9-12
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/expon.py
:language: python
:linenos:
:lineno-start: 14
:lines: 14-29
.. image:: ../../../images/expon_example1.png
:alt: Expon(1.5)
:align: center
Generating a translated Exponential(:math:`\lambda=1.5`) distribution with :math:`\text{loc} = 3`:
.. literalinclude:: ../../../examples/basic/expon.py
:language: python
:lineno-start: 32
:lines: 32
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/expon.py
:language: python
:lineno-start: 34
:lines: 34-49
.. image:: ../../../images/expon_example2.png
:alt: Expon(1.5, 3)
:align: center
"""
def __init__(
self,
amplitude: float = 1.0,
scale: float = 1.0,
loc: float = 0.0,
normalize: bool = False,
):
if not normalize and amplitude <= 0:
raise erH.NegativeAmplitudeError()
if scale <= 0:
raise erH.NegativeScaleError()
self.amplitude = 1 if normalize else amplitude
self.scale = scale
self.loc = loc
self.norm = normalize
[docs]
@classmethod
@md_scipy_like('1.0.7')
def scipy_like(cls, loc: float = 0.0, scale: float = 1.0) -> 'ExponentialDistribution':
r"""
Instantiate ExponentialDistribution with scipy parameterization.
Parameters
----------
loc: float, optional
The location parameter. Defaults to 0.0.
scale: float, optional
The rate parameter. Defaults to 1.0.
Returns
-------
ExponentialDistribution
A instance of normalized ExponentialDistribution.
"""
return cls(loc=loc, scale=scale, normalize=True)
[docs]
@classmethod
def from_scipy_params(cls, loc: float = 0.0, scale: float = 1.0) -> 'ExponentialDistribution':
r"""
Instantiate ExponentialDistribution with scipy parameterization.
Parameters
----------
loc: float, optional
The location parameter. Defaults to 0.0.
scale: float, optional
The rate parameter. Defaults to 1.0.
Returns
-------
ExponentialDistribution
A instance of normalized ExponentialDistribution.
"""
return cls(loc=loc, scale=scale, normalize=True)
[docs]
def pdf(self, x: np.ndarray) -> np.ndarray:
return exponential_pdf_(
x,
amplitude=self.amplitude,
lambda_=self.scale,
loc=self.loc,
normalize=self.norm,
)
[docs]
def logpdf(self, x: np.ndarray) -> np.ndarray:
return exponential_log_pdf_(
x,
amplitude=self.amplitude,
lambda_=self.scale,
loc=self.loc,
normalize=self.norm,
)
[docs]
def cdf(self, x: np.ndarray) -> np.ndarray:
return exponential_cdf_(
x,
amplitude=self.amplitude,
lambda_=self.scale,
loc=self.loc,
normalize=self.norm,
)
[docs]
def logcdf(self, x: np.ndarray) -> np.ndarray:
return exponential_log_cdf_(
x,
amplitude=self.amplitude,
lambda_=self.scale,
loc=self.loc,
normalize=self.norm,
)
[docs]
def stats(self) -> Dict[str, float]:
s, l_ = self.scale, self.loc
mean_ = (1 / s) + l_
median_ = (np.log(2) / s) + l_
mode_ = 0
variance_ = 1 / s**2
return {
"mean": mean_,
"median": median_,
"mode": mode_,
"variance": variance_,
"std": np.sqrt(variance_),
}