ChiSquare Distribution#

class ChiSquareDistribution(amplitude: float = 1.0, degree_of_freedom: int | float = 1, loc: float = 0.0, scale: float = 1.0, normalize: bool = False)[source]#

Bases: BaseDistribution

Class for ChiSquareDistribution distribution.

Note

The ChiSquareDistribution is a special case of the GammaDistribution,

\(\alpha\ (\text{shape}) = \text{dof} / 2\),
\(\theta\ (\text{scale}) = 2\).

Parameters:

amplitude (float, optional) – The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.
degree_of_freedom (int or float, optional) – The degree of freedom for the chi-square distribution. Default is 1.0.
loc (float, optional) – The location parameter, for shifting. Defaults to 0.0.
normalize (bool, optional) – If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Examples:

Importing libraries

import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import chi2

from pymultifit.distributions import ChiSquareDistribution

Generating a standard \(\chi^2(1)\) distribution with pyMultiFit and scipy.

x_values = np.linspace(start=0, stop=5, num=500)

y_multifit = ChiSquareDistribution(degree_of_freedom=1, normalize=True)
y_scipy = chi2

Plotting PDF and CDF

f, ax = plt.subplots(1, 2, figsize=(12, 5))

ax[0].plot(x_values, y_scipy.pdf(x=x_values, df=1), label="Scipy Chi2")
ax[0].plot(x_values, y_multifit.pdf(x_values), "k:", label="pyMultiFit Chi2")
ax[0].set_ylabel("f(x)")

ax[1].plot(x_values, y_scipy.cdf(x=x_values, df=1), label="Scipy Chi2")
ax[1].plot(x_values, y_multifit.cdf(x_values), "k:", label="pyMultiFit Chi2")
ax[1].set_ylabel("F(x)")

f.suptitle(r"$\chi^2$(1)")

for i in ax:
    i.set_xlabel("X")
    i.legend()
plt.tight_layout()

Generating a translated \(\chi^2(1)\) distribution with \(\text{loc} = 3\).

y_multifit = ChiSquareDistribution(degree_of_freedom=1, loc=3, normalize=True)

Plotting PDF and CDF

f, ax = plt.subplots(1, 2, figsize=(12, 5))

ax[0].plot(x_values, y_scipy.pdf(x=x_values, df=1, loc=3), label="Scipy translated Chi2")
ax[0].plot(x_values, y_multifit.pdf(x_values), "k:", label="pyMultiFit translated Chi2")
ax[0].set_ylabel("f(x)")

ax[1].plot(x_values, y_scipy.cdf(x=x_values, df=1, loc=3), label="Scipy translated Chi2")
ax[1].plot(x_values, y_multifit.cdf(x_values), "k:", label="pyMultiFit translated Chi2")
ax[1].set_ylabel("F(x)")

f.suptitle(r"$\chi^2$(1, loc=3)")

for i in ax:
    i.set_xlabel("X")
    i.legend()
plt.tight_layout()

Beta distribution (shifted and translated)

Attributes:

mean: The mean of the distribution.
median: The median of the distribution.
mode: The mode of the distribution.
stddev: The standard deviation of the distribution.
variance: The variance of the distribution.

Methods

`cdf`(x)	Compute the cumulative density function (CDF) for the distribution.
`from_scipy_params`(df[, loc, scale])	Instantiate ChiSquareDistribution with scipy parameterization.
`logcdf`(x)	Compute the log cumulative density function (logCDF) for the distribution.
`logpdf`(x)	Compute the log probability density function (logPDF) for the distribution.
`pdf`(x)	Compute the probability density function (PDF) for the distribution.
`scipy_like`(df[, loc, scale])	Instantiate ChiSquareDistribution with scipy parameterization.
`stats`()	Computes and returns the statistical properties of the distribution, including,

cdf(x: Annotated[ndarray[Any, dtype[float64]], '1D array']) → Annotated[ndarray[Any, dtype[float64]], '1D array'][source]#

Compute the cumulative density function (CDF) for the distribution.

Parameters:: x – Input array at which to evaluate the CDF.

classmethod from_scipy_params(df: int | float, loc: float = 0.0, scale: float = 1.0) → ChiSquareDistribution[source]#

Instantiate ChiSquareDistribution with scipy parameterization.

Parameters:

df: int or float: The degree of freedom for the ChiSquare distribution.
loc: float, optional: The location parameter. Defaults to 0.0.
scale: float, optional: The scale parameter. Defaults to 1.0

Returns:

ChiSquareDistribution: An instance of normalized ChiSquareDistribution.

logcdf(x: Annotated[ndarray[Any, dtype[float64]], '1D array']) → Annotated[ndarray[Any, dtype[float64]], '1D array'][source]#

Compute the log cumulative density function (logCDF) for the distribution.

Parameters:: x – Input array at which to evaluate the logCDF.

logpdf(x: Annotated[ndarray[Any, dtype[float64]], '1D array']) → Annotated[ndarray[Any, dtype[float64]], '1D array'][source]#

Compute the log probability density function (logPDF) for the distribution.

Parameters:: x – Input array at which to evaluate the logPDF.

pdf(x: Annotated[ndarray[Any, dtype[float64]], '1D array']) → Annotated[ndarray[Any, dtype[float64]], '1D array'][source]#

Compute the probability density function (PDF) for the distribution.

Parameters:: x – Input array at which to evaluate the PDF.

classmethod scipy_like(df: int | float, loc: float = 0.0, scale: float = 1.0) → ChiSquareDistribution[source]#

Instantiate ChiSquareDistribution with scipy parameterization.

Parameters:

df: int or float: The degree of freedom for the ChiSquare distribution.
loc: float, optional: The location parameter. Defaults to 0.0.
scale: float, optional: The scale parameter. Defaults to 1.0

Returns:

ChiSquareDistribution: An instance of normalized ChiSquareDistribution.

Deprecated since version v1.0.7: Use from_scipy_params instead of scipy_like. scipy_like will be removed in a future release.

stats() → Dict[str, float][source]#

Computes and returns the statistical properties of the distribution, including,

mean,
median,
variance, and
standard deviation.

Returns:: A dictionary containing statistical properties such as mean, variance, etc.
Return type:: Dict[str, float]

Notes

If any of the parameters is not computable for a distribution, this method returns None.

property mean: float | None#: The mean of the distribution.

property median: float | None#: The median of the distribution.

property mode: float | None#: The mode of the distribution.

property stddev: float | None#: The standard deviation of the distribution.

property variance: float | None#: The variance of the distribution.

This class internally utilizes the following functions from utilities_d module:

gamma_sr_pdf_()
gamma_sr_cdf_()

Recommended Import#

from pymultifit.distributions import ChiSquareDistribution

Full Import#

from pymultifit.distributions.chiSquare_d import ChiSquareDistribution