Distribution utilities

Created on Aug 03 17:13:21 2024

The utilities_d module serves as a cornerstone of the pyMultiFit library, containing majority of the core utility functions utilized across various classes and components. It provides a comprehensive suite of mathematical and statistical tools, including probability distribution functions (PDFs), cumulative distribution functions (CDFs), some internal scaling and masking utilities, and data preprocessing methods.

Available for user

arc_sine_pdf_(x: ndarray, amplitude: float = 1.0, loc: float = 0.0, scale: float = 1.0, normalize: bool = False) → ndarray

Compute PDF of ArcSineDistribution.

Parameters:

xnp.ndarray

Input array of values where PDF is evaluated.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

locfloat, optional

The location parameter specifying the lower bound of the distribution. Defaults to 0.0.

scalefloat, optional

The scale parameter, specifying the width of the distribution. Defaults to 1.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated PDF values.

Notes

The ArcSine PDF is defined as:

\[f(y) = \frac{1}{\pi \sqrt{y(1-y)}}\]

where, \(y\) is the transformed value of \(x\), defined as:

\[y = \frac{x - \text{loc}}{\text{scale}}\]

The final PDF is expressed as \(f(y)/\text{scale}\).

beta_pdf_(x: ndarray, amplitude: float = 1.0, alpha: float = 1.0, beta: float = 1.0, loc: float = 0.0, scale: float = 1.0, normalize: bool = False) → ndarray

Compute PDF of BetaDistribution.

Parameters:

xnp.ndarray

Input array of values where PDF is evaluated.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

alphafloat, optional

The \(\alpha\) parameter. Default is 1.0.

betafloat, optional

The \(\beta\) parameter. Default is 1.0.

locfloat, optional

The location parameter, for shifting. Default is 0.0.

scalefloat, optional

The scale parameter, for scaling. Default is 1.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as x, containing the evaluated PDF values.

Notes

The Beta PDF is defined as:

\[f(y; \alpha, \beta) = \frac{y^{\alpha - 1} (1 - y)^{\beta - 1}}{B(\alpha, \beta)}\]

where \(B(\alpha, \beta)\) is the Beta function (see, scipy.special.beta), and \(y\) is the transformed value of \(x\) such that:

\[y = \frac{x - \text{loc}}{\text{scale}}\]

The final PDF is expressed as \(f(y)/\text{scale}\).

beta_cdf_(x: ndarray, amplitude: float = 1.0, alpha: float = 1.0, beta: float = 1.0, loc: float = 0.0, scale: float = 1.0, normalize: bool = False) → ndarray

Compute CDF for BetaDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

For API consistency only.

alphafloat, optional

The \(\alpha\) parameter. Default is 1.0.

betafloat, optional

The \(\beta\) parameter. Default is 1.0.

locfloat, optional

The location parameter, for shifting. Default is 0.0.

scalefloat, optional

The scale parameter, for scaling. Default is 1.0.

normalizebool, optional

For API consistency only.

Returns:

np.ndarray

Array of the same shape as x, containing the evaluated PDF values.

Notes

The Beta CDF is defined as:

\[I_x(\alpha, \beta)\]

where \(I_x(\alpha, \beta)\) is the regularized incomplete Beta function, see betainc.

chi_square_pdf_(x: ndarray, amplitude: float = 1.0, degree_of_freedom: int | float = 1, loc: float = 0.0, scale: float = 1.0, normalize: bool = False) → ndarray

Compute PDF for ChiSquareDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

degree_of_freedomint, optional

The degrees of freedom parameter. Defaults to 1.

locfloat, optional

The location parameter, for shifting. Defaults to 0.0.

scale: float, optional

The scale parameter, for scaling. Defaults to 1.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The ChiSquare PDF is defined as:

\[f(y\ |\ k) = \dfrac{y^{(k/2) - 1} e^{-y/2}}{2^{k/2} \Gamma(k/2)}\]

where \(\Gamma(k)\) is the gamma function, and \(y\) is the transformed value of \(x\), defined as:

\[y = x - \text{loc}\]

The final PDF is expressed as \(f(y)\).

exponential_pdf_(x: ndarray, amplitude: float = 1.0, lambda_: float = 1.0, loc: float = 0.0, normalize: bool = False) → ndarray

Compute PDF for ExponentialDistribution.

Note

This function uses gamma_sr_pdf_() to calculate the PDF with \(\alpha = 1\) and \(\lambda_\text{gammaSR} = \lambda_\text{expon}\).

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

lambda_float, optional

The scale parameter, \(\lambda\). Defaults to 1.0.

locfloat, optional

The location parameter, for shifting. Defaults to 0.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The Exponential PDF is defined as:

\[\begin{split}f(y, \lambda) = \begin{cases} \lambda \exp\left[-\lambda y\right] &; y \geq 0, \\ 0 &; y < 0. \end{cases}\end{split}\]

where, \(y\) is the transformed value of \(x\), defined as:

\[y = x - \text{loc}\]

The final PDF is expressed as \(f(y)\).

exponential_cdf_(x: ndarray, amplitude: float = 1.0, scale: float = 1.0, loc: float = 0.0, normalize: bool = False) → ndarray

Compute CDF of ExponentialDistribution.

Note

This function uses gamma_sr_cdf_() to calculate the CDF with \(\alpha = 1\) and \(\lambda_\text{gammaSR} = \lambda_\text{expon}\).

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

For API consistency only.

lambda_float, optional

The scale parameter, \(\lambda\). Defaults to 1.0.

locfloat, optional

The location parameter, for shifting. Defaults to 0.0.

normalizebool, optional

For API consistency only.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The Exponential CDF is defined as:

\[F(x) = 1 - \exp\left[-\lambda x\right].\]

folded_normal_pdf_(x: ndarray, amplitude: float = 1.0, mean: float = 0.0, sigma: float = 1.0, loc: float = 0.0, normalize: bool = False) → ndarray

Compute PDF for FoldedNormalDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

meanfloat, optional

The mean parameter, \(\mu\). Defaults to 0.0.

sigmafloat, optional

The standard deviation parameter, \(\sigma\). Defaults to 1.0.

locfloat, optional

The location parameter, for shifting. Defaults to 0.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The FoldedNormal PDF is defined as:

\[f(y\ |\ \mu, \sigma) = \phi(y\ |\ \mu, 1) + \phi(y\ |\ -\mu, 1),\]

where \(\phi\) is the PDF of GaussianDistribution, and \(y\) is the transformed value of \(x\), defined as:

\[y = \dfrac{x - \text{loc}}{\sigma}\]

The final PDF is expressed as \(f(y)/\sigma\).

folded_normal_cdf_(x: ndarray, amplitude: float = 1.0, mean: float = 0.0, sigma: float = 1.0, loc: float = 0.0, normalize: bool = False) → ndarray

Compute CDF for FoldedNormalDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitude: float, optional

For API consistency only.

meanfloat, optional

The mean parameter, \(\mu\). Defaults to 0.0.

sigmafloat, optional

The standard deviation parameter, \(\sigma\). Defaults to 1.0.

locfloat, optional

The location parameter, for shifting. Defaults to 0.0.

normalize: bool, optional

For API consistency only.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The FoldedNormal CDF is defined as:

\[F(y) = \Phi(y\ | \mu, 1) + \Phi(y\ | -\mu, 1) - 1\]

where \(\Phi\) is the CDF of GaussianDistribution, and \(y\) is the transformed value of \(x\), defined as:

\[y = \dfrac{x - \text{loc}}{\sigma}\]

gamma_sr_pdf_(x: ndarray, amplitude: float = 1.0, alpha: float = 1.0, lambda_: float = 1.0, loc: float = 0.0, normalize: bool = False) → ndarray

Compute PDF for GammaDistributionSR with \(\alpha\) (shape) and \(\lambda\) (rate) parameters.

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

alphafloat, optional

The shape parameter, \(\alpha\). Defaults to 1.0.

lambda_float, optional

The rate parameter, \(\lambda\). Defaults to 1.0.

locfloat, optional

The location parameter, for shifting. Defaults to 0.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated PDF values.

Notes

The Gamma SR PDF is defined as:

\[\begin{split}f(y; \alpha, \lambda) = \begin{cases} \dfrac{\lambda^\alpha}{\Gamma(\alpha)} y^{\alpha - 1} \exp\left[-\lambda y\right], & y > \text{loc}, \\ 0, & y \leq \text{loc}. \end{cases}\end{split}\]

where \(y\) is the transformed value of \(x\), defined as:

\[y = x - \text{loc}\]

The final PDF is expressed as \(f(y)\).

gamma_sr_cdf_(x: ndarray, amplitude: float = 1.0, alpha: float = 1.0, lambda_: float = 1.0, loc: float = 0.0, normalize: bool = False) → ndarray

Compute CDF for GammaDistributionSR with \(\alpha\) and \(\lambda\) parameters.

Parameters:

xnp.ndarray

Input array of values.

amplitude: float, optional

For API consistency only.

alphafloat, optional

The shape parameter, \(\alpha\). Defaults to 1.0.

lambda_float, optional

The rate parameter, \(\lambda\). Defaults to 1.0.

locfloat, optional

The location parameter, for shifting. Defaults to 0.0.

normalize: float, optional

For API consistency only.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated PDF values.

Notes

The Gamma CDF is defined as:

\[F(x) = \dfrac{1}{\Gamma(\alpha)}\gamma(\alpha, \lambda x)\]

where, \(\gamma(\alpha, \lambda x)\) is the lower incomplete gamma function, see gammainc.

gamma_ss_pdf_(x: ndarray, amplitude: float = 1.0, alpha: float = 1.0, theta: float = 1.0, normalize: bool = False) → ndarray

Compute PDF for GammaDistributionSS with \(\alpha\) (shape) and \(\theta\) (scale) parameters.

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

alphafloat, optional

The shape parameter, \(\alpha\). Defaults to 1.0.

thetafloat, optional

The scale parameter, \(\lambda\). Defaults to 1.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The Gamma SS PDF is defined as:

\[f(y\ |\ \alpha, \theta) = \dfrac{1}{\Gamma(\alpha)\theta^\alpha}y^{\alpha-1}\exp\left[-\dfrac{y}{\theta}\right]\]

where \(y\) is the transformed value of \(x\), defined as:

\[y = x - \text{loc}\]

The final PDF is expressed as \(f(y)\).

gaussian_pdf_(x: ndarray, amplitude: float = 1.0, mean: float = 0.0, std: float = 1.0, normalize: bool = False) → ndarray

Compute PDF for the GaussianDistribution

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

meanfloat, optional

The mean parameter, \(\mu\). Defaults to 0.0.

stdfloat, optional

The standard deviation parameter, \(\sigma\). Defaults to 1.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The Gaussian PDF is defined as:

\[f(x; \mu, \sigma) = \phi\left(\dfrac{x-\mu}{\sigma}\right) = \dfrac{1}{\sqrt{2\pi\sigma}}\exp\left[-\dfrac{1}{2}\left(\dfrac{x-\mu}{\sigma}\right)^2\right]\]

The final PDF is expressed as \(f(x)\).

gaussian_cdf_(x: ndarray, amplitude: float = 1.0, mean: float = 0.0, std: float = 1.0, normalize: bool = False) → ndarray

Compute CDF for the GaussianDistribution

Parameters:

xnp.ndarray

Input array of values.

amplitude: float, optional

For API consistency only.

meanfloat, optional

The mean parameter, \(\mu\). Defaults to 0.0.

stdfloat, optional

The standard deviation parameter, \(\sigma\). Defaults to 1.0.

normalize: float, optional

For API consistency only.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The Gaussian CDF is defined as:

\[F(x) = \Phi\left(\dfrac{x-\mu}{\sigma}\right) = \dfrac{1}{2} \left[1 + \text{erf}\left(\dfrac{x - \mu}{\sigma\sqrt{2}}\right)\right]\]

half_normal_pdf_(x: ndarray, amplitude: float = 1.0, sigma: float = 1.0, loc: float = 0.0, normalize: bool = False) → ndarray

Compute PDF for the HalfNormalDistribution.

Note

The HalfNormalDistribution. is a special case of the FoldedNormalDistribution with \(\mu = 0\).

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

sigmafloat, optional

The standard deviation \(\sigma\). Defaults to 1.0.

locfloat, optional

The location parameter, for shifting. Defaults to 0.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The HalfNormal PDF is defined as:

\[f(x\ |\ \sigma) = \sqrt{\dfrac{2}{\pi\sigma^2}}\exp\left[-\dfrac{x^2}{2\sigma^2}\right]\]

where \(x >= 0\).

half_normal_cdf_(x: ndarray, amplitude: float = 1.0, scale: float = 1.0, loc: float = 0.0, normalize: bool = False) → ndarray

Compute the CDF for HalfNormalDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitude: float, optional

For API consistency only.

sigmafloat, optional

The standard deviation \(\sigma\). Defaults to 1.0.

locfloat, optional

The location parameter, for shifting. Defaults to 0.0.

normalize: float, optional

For API consistency only.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The HalfNormal CDF is defined as:

\[F(x) = \text{erf}\left( \frac{x}{\sqrt{2\sigma^2}}\right)\]

laplace_pdf_(x: ndarray, amplitude: float = 1.0, mean: float = 0.0, diversity: float = 1.0, normalize: bool = False) → ndarray

Compute PDF for LaplaceDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

meanfloat, optional

The mean parameter, \(\mu\). Defaults to 0.0.

diversityfloat, optional

The diversity parameter, \(b\). Defaults to 1.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The Laplace PDF is defined as:

\[f(x\ |\ \mu, b) = \dfrac{1}{2b}\exp\left(-\dfrac{|x - \mu|}{b}\right)\]

The final PDF is expressed as \(f(x)\).

laplace_cdf_(x: ndarray, amplitude: float = 1.0, mean: float = 0.0, diversity: float = 1.0, normalize: bool = False) → ndarray

Compute CDF for LaplaceDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitude: float, optional

For API consistency only.

meanfloat, optional

The mean parameter, \(\mu\). Defaults to 0.0.

diversityfloat, optional

The diversity parameter, \(b\). Defaults to 1.0.

normalize: bool, optional

For API consistency only.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The Laplace CDF is defined as:

\[\begin{split}F(x) = \begin{cases} \dfrac{1}{2}\exp\left(\dfrac{x-\mu}{b}\right) &,&x\leq\mu\\ 1 - \dfrac{1}{2}\exp\left(-\dfrac{x-\mu}{b}\right) &,&x\geq\mu \end{cases}\end{split}\]

log_normal_pdf_(x: ndarray, amplitude: float = 1.0, mean: float = 0.0, std: float = 1.0, loc: float = 0.0, normalize: bool = False) → ndarray

Compute PDF for LogNormalDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

meanfloat, optional

The mean parameter, \(\mu\). Defaults to 0.0.

stdfloat, optional

The standard deviation parameter, \(\sigma\). Defaults to 1.0.

locfloat, optional

The location parameter, for shifting. Defaults to 0.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The LogNormal PDF is defined as:

\[f(y\ |\ \mu, \sigma) = \dfrac{1}{\sigma y\sqrt{2\pi}}\exp\left(-\dfrac{(\ln y - \mu)^2}{2\sigma^2}\right)\]

where, \(y\) is the transformed value of \(x\), defined as:

\[y = x - \text{loc}\]

The final PDF is expressed as \(f(y)\).

log_normal_cdf_(x: ndarray, amplitude: float = 1.0, mean: float = 0.0, std=1.0, loc: float = 0.0, normalize: bool = False) → ndarray

Compute CDF of LogNormalDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitude: float, optional

For API consistency only.

meanfloat, optional

The mean parameter, \(\mu\). Defaults to 0.0.

stdfloat, optional

The standard deviation parameter, \(\sigma\). Defaults to 1.0.

locfloat, optional

The location parameter, for shifting. Defaults to 0.0.

normalize: bool, optional

For API consistency only

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The LogNormal CDF is defined as:

\[F(x) = \Phi\left(\dfrac{\ln x - \mu}{\sigma}\right)\]

skew_normal_pdf_(x: ndarray, amplitude: float = 1.0, shape: float = 0.0, loc: float = 0.0, scale: float = 1.0, normalize: bool = False) → ndarray

Compute PDF of SkewNormalDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

shapefloat, optional

The shape parameter, \(\alpha\). Defaults to 0.0.

locfloat, optional

The location parameter, \(\xi\). Defaults to 0.0.

scale: float, optional

The scale parameter, \(\omega\) Defaults to 1.0,

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The SkewNormal PDF is defined as:

\[f(y\ |\ \alpha, \xi, \omega) = 2\phi(y)\Phi(\alpha y)\]

where, \(\phi(y)\) and \(\Phi(\alpha y)\) are the GaussianDistribution PDF and CDF defined at \(y\) and \(\alpha y\) respectively. Additionally, \(y\) is the transformed value of \(x\), defined as:

\[y = \dfrac{x - \xi}{\omega}\]

The final PDF is expressed as \(f(y)/\omega\).

skew_normal_cdf_(x: ndarray, amplitude: float = 1.0, shape: float = 0.0, loc: float = 0.0, scale: float = 1.0, normalize: bool = False)

Compute CDF of SkewNormalDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitude: float, optional

For API consistency only.

shapefloat, optional

The shape parameter, \(\alpha\). Defaults to 0.0.

locfloat, optional

The location parameter, \(\xi\). Defaults to 0.0.

scale: float, optional

The scale parameter, \(\omega\) Defaults to 1.0,

normalize: float, optional

For API consistency only.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The SkewNormal CDF is defined as:

\[F(x) = \Phi\left(\dfrac{x - \xi}{\omega}\right) - 2T\left(\dfrac{x - \xi}{\omega}, \alpha\right)\]

where, \(T\) is the Owen’s T function, see scipy.special.owens_t, and \(\Phi(\cdot)\) is the GaussianDistribution CDF function.

uniform_pdf_(x: ndarray, amplitude: float = 1.0, low: float = 0.0, high: float = 1.0, normalize: bool = False) → ndarray

Compute PDF of UniformDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitudefloat, optional

The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

lowfloat, optional

The lower bound, \(a\). Defaults to 0.0.

highfloat, optional

The upper bound, \(b\). Defaults to 1.0.

normalizebool, optional

If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The Uniform PDF is defined as:

\[f(x\ |\ a, b) = \dfrac{1}{b-a}\]

uniform_cdf_(x: ndarray, amplitude: float = 1.0, low: float = 0.0, high: float = 1.0, normalize: bool = False) → ndarray

Compute CDF of UniformDistribution.

Parameters:

xnp.ndarray

Input array of values.

amplitude: float, optional

For API consistency only.

lowfloat, optional

The lower bound, \(a\). Defaults to 0.0.

highfloat, optional

The upper bound, \(b\). Defaults to 1.0.

normalize: bool, optional

For API consistency only.

Returns:

np.ndarray

Array of the same shape as \(x\), containing the evaluated values.

Notes

The Uniform CDF is defined as:

\[\begin{split}F(x) = \begin{cases} 0 &, x < a\\ \dfrac{x-a}{b-a} &, x \in [a, b]\\ 1 &, x > b \end{cases}\end{split}\]

Internal functions

_beta_masking(y: ndarray, alpha: float, beta: float) → ndarray

Creates a mask for beta distributions to identify out-of-range or undefined values.

Parameters:

ynp.ndarray

Array of values to check, typically in the range [0, 1].

alphafloat

Alpha parameter of the beta distribution. Determines the shape of the distribution.

betafloat

Beta parameter of the beta distribution. Determines the shape of the distribution.

Returns:

np.ndarray

A boolean mask array where True indicates out-of-range or undefined values.

_pdf_scaling(pdf_: ndarray, amplitude: float) → ndarray

Scales a probability density function (PDF) by a given amplitude.

Parameters:

pdf_np.ndarray

The input PDF array to be scaled.

amplitudefloat

The amplitude to scale the PDF.

Returns:

np.ndarray

The scaled PDF array.

_remove_nans(x: ndarray) → ndarray

Replaces NaN, positive infinity, and negative infinity values in an array.

Parameters:

xnp.ndarray

Input array that may contain NaN, positive infinity, or negative infinity values.

Returns:

np.ndarray

Array with NaN replaced by 0, positive infinity replaced by np.inf, and negative

infinity replaced by -np.inf.