Beta Distribution#

class BetaDistribution(amplitude: float = 1.0, alpha: float = 1.0, beta: float = 1.0, loc: float = 0.0, scale: float = 1.0, normalize: bool = False)[source]#

Bases: BaseDistribution

Class for Beta distribution.

Parameters:

amplitude (float, optional) – The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.
alpha (float, optional) – The \(\alpha\) parameter. Defaults to 1.0.
beta (float, optional) – The \(\beta\) parameter. Defaults to 1.0.
loc (float, optional) – float, optional The location parameter, for shifting. Defaults to 0.0.
scale (float, optional) – float, optional The scale parameter, for scaling. Defaults to 1.0.
normalize (bool, optional) – bool, optional If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Raises:

NegativeAmplitudeError – If the provided value of amplitude is negative.
NegativeAlphaError – If the provided value of \(\alpha\) is negative.
NegativeBetaError – If the provided value of \(\beta\) is negative.

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.
`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`(a, b[, loc, scale])	Instantiate BetaDistribution with scipy parameterization.
`stats`()	Computes and returns the statistical properties of the distribution, including,

Examples

Importing libraries

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

from pymultifit.distributions import BetaDistribution

Generating a standard \(\text{Beta}(2, 30)\) distribution with pyMultiFit and scipy.

x_values = np.linspace(start=0, stop=1, num=500)

y_multifit = BetaDistribution(alpha=2, beta=30, normalize=True)
y_scipy = beta

Plotting PDF and CDF

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

ax[0].plot(x_values, y_scipy.pdf(x=x_values, a=2, b=30), label='Scipy Beta')
ax[0].plot(x_values, y_multifit.pdf(x_values), 'k:', label='pyMultiFit Beta')
ax[0].set_ylabel('f(x)')

ax[1].plot(x_values, y_scipy.cdf(x=x_values, a=2, b=30), label='Scipy Beta')
ax[1].plot(x_values, y_multifit.cdf(x_values), 'k:', label='pyMultiFit Beta')
ax[1].set_ylabel('F(x)')

f.suptitle('Beta(2, 30)')

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

Generating a shifted and translated \(\text{Beta}(2, 30)\) distribution.

x_values = np.linspace(start=0, stop=10, num=500)

y_multifit = BetaDistribution(alpha=2, beta=30, loc=3, scale=5, normalize=True)
y_scipy = beta

Plotting PDF and CDF

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

ax[0].plot(x_values, y_scipy.pdf(x=x_values, a=2, b=30, loc=3, scale=5), label='Scipy Beta scaled')
ax[0].plot(x_values, y_multifit.pdf(x_values), 'k:', label='pyMultiFit Beta scaled')
ax[0].set_ylabel('f(x)')

ax[1].plot(x_values, y_scipy.cdf(x=x_values, a=2, b=30, loc=3, scale=5), label='Scipy Beta scaled')
ax[1].plot(x_values, y_multifit.cdf(x_values), 'k:', label='pyMultiFit Beta scaled')
ax[1].set_ylabel('F(x)')

f.suptitle('Beta(2, 30, 5, 3)')

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

Beta distribution (shifted and translated)

cdf(x)[source]#

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

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

logcdf(x)[source]#

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

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

logpdf(x)[source]#

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

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

pdf(x)[source]#

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

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

classmethod scipy_like(a: float, b: float, loc: float = 0.0, scale: float = 1.0)[source]#

Instantiate BetaDistribution with scipy parameterization.

Parameters:

a: float: The shape parameter, \(\alpha\).
b: float: The shape parameter, \(\beta\).
loc: float, optional: The location parameter. Defaults to 0.0.
scale: float, optional: The scale parameter,. Defaults to 1.0.

Returns:

BetaDistribution: An instance of normalized BetaDistribution.

stats()[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 parameter is not computable for a distribution, this method returns None.

property mean#: The mean of the distribution.

property median#: The median of the distribution.

property mode#: The mode of the distribution.

property stddev#: The standard deviation of the distribution.

property variance#: The variance of the distribution.

Note

The BetaDistribution encompasses the following specific cases:

ArcSineDistribution:
- \(\alpha = \beta = 0.5\)

UniformDistribution:
- \(\alpha = \beta = 1\)

This class internally utilizes the following functions from utilities_d module:

Recommended Import#

from pymultifit.distributions import BetaDistribution

Full Import#

from pymultifit.distributions.beta_d import BetaDistribution