HalfNormal Distribution

class HalfNormalDistribution(amplitude: float = 1.0, scale: float = 1.0, loc: float = 0.0, normalize: bool = False)

Bases: FoldedNormalDistribution

Class for halfnormal distribution.

Parameters:

• amplitude (float, optional) – The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

• scale (float, optional) – The standard deviation parameter, \(\sigma\). Defaults to 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.

Raises:

• NegativeAmplitudeError – If the provided value of amplitude is negative.

• NegativeStandardDeviationError – If the provided value of standard deviation 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.
pdf(x)	Compute the probability density function (PDF) for the distribution.
scipy_like([loc, scale])	Instantiate HalfNormalDistribution with scipy parametrization.
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 halfnorm

from pymultifit.distributions import HalfNormalDistribution

Generating a standard Half Normal(\(\sigma = 1\)) distribution with pyMultiFit and scipy:

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

y_multifit = HalfNormalDistribution(normalize=True)
y_scipy = halfnorm

Plotting PDF and CDF:

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

ax[0].plot(x_values, y_scipy.pdf(x=x_values), label='Scipy Half Normal')
ax[0].plot(x_values, y_multifit.pdf(x_values), 'k:', label='pyMultiFit Half Normal')
ax[0].set_ylabel('f(x)')

ax[1].plot(x_values, y_scipy.cdf(x=x_values), label='Scipy Half Normal')
ax[1].plot(x_values, y_multifit.cdf(x_values), 'k:', label='pyMultiFit Half Normal')
ax[1].set_ylabel('F(x)')

f.suptitle('Half Normal(1)')

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

Generating a translated Gaussian(\(\sigma=3\)) distribution with \(\text{loc}=3\):

y_multifit = HalfNormalDistribution(loc=3, scale=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, scale=3, loc=3), label='Scipy translated Half Normal')
ax[0].plot(x_values, y_multifit.pdf(x_values), 'k:', label='pyMultiFit translated Half Normal')
ax[0].set_ylabel('f(x)')

ax[1].plot(x_values, y_scipy.cdf(x=x_values, scale=3, loc=3), label='Scipy translated Half Normal')
ax[1].plot(x_values, y_multifit.cdf(x_values), 'k:', label='pyMultiFit translated Half Normal')
ax[1].set_ylabel('F(x)')

f.suptitle(r'Half Normal(3, 3)')

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

cdf(x: ndarray) → ndarray

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

Parameters:

x – Input array at which to evaluate the CDF.

pdf(x: ndarray) → ndarray

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

Parameters:

x – Input array at which to evaluate the PDF.

classmethod scipy_like(loc: float = 0.0, scale: float = 1.0)

Instantiate HalfNormalDistribution with scipy parametrization.

Parameters:

loc: float, optional

The location parameter. Defaults to 0.0.

scale: float, optional

The scale parameter. Defaults to 1.0.

Returns:

HalfNormalDistribution

An instance of normalized HalfNormalDistribution.

stats() → Dict[str, Any]

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

1. mean,

2. median,

3. variance, and

4. 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.

This class internally utilizes the following functions from utilities_d module:

• half_normal_pdf_

• half_normal_cdf_

Recommended Import

from pymultifit.distributions import HalfNormalDistribution

Full Import

from pymultifit.distributions.halfNormal_d import HalfNormalDistribution