// <copyright file="Stable.cs" company="Math.NET">
|
// Math.NET Numerics, part of the Math.NET Project
|
// http://numerics.mathdotnet.com
|
// http://github.com/mathnet/mathnet-numerics
|
//
|
// Copyright (c) 2009-2013 Math.NET
|
//
|
// Permission is hereby granted, free of charge, to any person
|
// obtaining a copy of this software and associated documentation
|
// files (the "Software"), to deal in the Software without
|
// restriction, including without limitation the rights to use,
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
// copies of the Software, and to permit persons to whom the
|
// Software is furnished to do so, subject to the following
|
// conditions:
|
//
|
// The above copyright notice and this permission notice shall be
|
// included in all copies or substantial portions of the Software.
|
//
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
// OTHER DEALINGS IN THE SOFTWARE.
|
// </copyright>
|
|
using System;
|
using System.Collections.Generic;
|
using IStation.Numerics.Random;
|
|
namespace IStation.Numerics.Distributions
|
{
|
/// <summary>
|
/// Continuous Univariate Stable distribution.
|
/// A random variable is said to be stable (or to have a stable distribution) if it has
|
/// the property that a linear combination of two independent copies of the variable has
|
/// the same distribution, up to location and scale parameters.
|
/// For details about this distribution, see
|
/// <a href="http://en.wikipedia.org/wiki/Stable_distribution">Wikipedia - Stable distribution</a>.
|
/// </summary>
|
public class Stable : IContinuousDistribution
|
{
|
System.Random _random;
|
|
readonly double _alpha;
|
readonly double _beta;
|
readonly double _scale;
|
readonly double _location;
|
|
/// <summary>
|
/// Initializes a new instance of the <see cref="Stable"/> class.
|
/// </summary>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
public Stable(double alpha, double beta, double scale, double location)
|
{
|
if (!IsValidParameterSet(alpha, beta, scale, location))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
_random = SystemRandomSource.Default;
|
_alpha = alpha;
|
_beta = beta;
|
_scale = scale;
|
_location = location;
|
}
|
|
/// <summary>
|
/// Initializes a new instance of the <see cref="Stable"/> class.
|
/// </summary>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
|
public Stable(double alpha, double beta, double scale, double location, System.Random randomSource)
|
{
|
if (!IsValidParameterSet(alpha, beta, scale, location))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
_random = randomSource ?? SystemRandomSource.Default;
|
_alpha = alpha;
|
_beta = beta;
|
_scale = scale;
|
_location = location;
|
}
|
|
/// <summary>
|
/// A string representation of the distribution.
|
/// </summary>
|
/// <returns>a string representation of the distribution.</returns>
|
public override string ToString()
|
{
|
return $"Stable(α = {_alpha}, β = {_beta}, c = {_scale}, μ = {_location})";
|
}
|
|
/// <summary>
|
/// Tests whether the provided values are valid parameters for this distribution.
|
/// </summary>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
public static bool IsValidParameterSet(double alpha, double beta, double scale, double location)
|
{
|
return alpha > 0.0 && alpha <= 2.0 && beta >= -1.0 && beta <= 1.0 && scale > 0.0 && !double.IsNaN(location);
|
}
|
|
/// <summary>
|
/// Gets the stability (α) of the distribution. Range: 2 ≥ α > 0.
|
/// </summary>
|
public double Alpha => _alpha;
|
|
/// <summary>
|
/// Gets The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.
|
/// </summary>
|
public double Beta => _beta;
|
|
/// <summary>
|
/// Gets the scale (c) of the distribution. Range: c > 0.
|
/// </summary>
|
public double Scale => _scale;
|
|
/// <summary>
|
/// Gets the location (μ) of the distribution.
|
/// </summary>
|
public double Location => _location;
|
|
/// <summary>
|
/// Gets or sets the random number generator which is used to draw random samples.
|
/// </summary>
|
public System.Random RandomSource
|
{
|
get => _random;
|
set => _random = value ?? SystemRandomSource.Default;
|
}
|
|
/// <summary>
|
/// Gets the mean of the distribution.
|
/// </summary>
|
public double Mean
|
{
|
get
|
{
|
if (_alpha <= 1d)
|
{
|
throw new NotSupportedException();
|
}
|
|
return _location;
|
}
|
}
|
|
/// <summary>
|
/// Gets the variance of the distribution.
|
/// </summary>
|
public double Variance
|
{
|
get
|
{
|
if (_alpha == 2d)
|
{
|
return 2.0*_scale*_scale;
|
}
|
|
return double.PositiveInfinity;
|
}
|
}
|
|
/// <summary>
|
/// Gets the standard deviation of the distribution.
|
/// </summary>
|
public double StdDev
|
{
|
get
|
{
|
if (_alpha == 2d)
|
{
|
return Constants.Sqrt2*_scale;
|
}
|
|
return double.PositiveInfinity;
|
}
|
}
|
|
/// <summary>
|
/// Gets he entropy of the distribution.
|
/// </summary>
|
/// <remarks>Always throws a not supported exception.</remarks>
|
public double Entropy => throw new NotSupportedException();
|
|
/// <summary>
|
/// Gets the skewness of the distribution.
|
/// </summary>
|
/// <remarks>Throws a not supported exception of <c>Alpha</c> != 2.</remarks>
|
public double Skewness
|
{
|
get
|
{
|
if (_alpha != 2d)
|
{
|
throw new NotSupportedException();
|
}
|
|
return 0.0;
|
}
|
}
|
|
/// <summary>
|
/// Gets the mode of the distribution.
|
/// </summary>
|
/// <remarks>Throws a not supported exception if <c>Beta != 0</c>.</remarks>
|
public double Mode
|
{
|
get
|
{
|
if (_beta != 0d)
|
{
|
throw new NotSupportedException();
|
}
|
|
return _location;
|
}
|
}
|
|
/// <summary>
|
/// Gets the median of the distribution.
|
/// </summary>
|
/// <remarks>Throws a not supported exception if <c>Beta != 0</c>.</remarks>
|
public double Median
|
{
|
get
|
{
|
if (_beta != 0)
|
{
|
throw new NotSupportedException();
|
}
|
|
return _location;
|
}
|
}
|
|
/// <summary>
|
/// Gets the minimum of the distribution.
|
/// </summary>
|
public double Minimum
|
{
|
get
|
{
|
if (Math.Abs(_beta) == 1)
|
{
|
return 0.0;
|
}
|
|
return double.NegativeInfinity;
|
}
|
}
|
|
/// <summary>
|
/// Gets the maximum of the distribution.
|
/// </summary>
|
public double Maximum => double.PositiveInfinity;
|
|
/// <summary>
|
/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
|
/// </summary>
|
/// <param name="x">The location at which to compute the density.</param>
|
/// <returns>the density at <paramref name="x"/>.</returns>
|
public double Density(double x)
|
{
|
return PDF(_alpha, _beta, _scale, _location, x);
|
}
|
|
/// <summary>
|
/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
|
/// </summary>
|
/// <param name="x">The location at which to compute the log density.</param>
|
/// <returns>the log density at <paramref name="x"/>.</returns>
|
public double DensityLn(double x)
|
{
|
return PDFLn(_alpha, _beta, _scale, _location, x);
|
}
|
|
/// <summary>
|
/// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
|
/// </summary>
|
/// <param name="x">The location at which to compute the cumulative distribution function.</param>
|
/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
|
/// <remarks>Throws a not supported exception if <c>Alpha != 2</c>, <c>(Alpha != 1 and Beta !=0)</c>, or <c>(Alpha != 0.5 and Beta != 1)</c></remarks>
|
public double CumulativeDistribution(double x)
|
{
|
return CDF(_alpha, _beta, _scale, _location, x);
|
}
|
|
/// <summary>
|
/// Samples the distribution.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
/// <returns>a random number from the distribution.</returns>
|
static double SampleUnchecked(System.Random rnd, double alpha, double beta, double scale, double location)
|
{
|
var randTheta = ContinuousUniform.Sample(rnd, -Constants.PiOver2, Constants.PiOver2);
|
var randW = Exponential.Sample(rnd, 1.0);
|
|
if (!1.0.AlmostEqual(alpha))
|
{
|
var theta = (1.0/alpha)*Math.Atan(beta*Math.Tan(Constants.PiOver2*alpha));
|
var angle = alpha*(randTheta + theta);
|
var part1 = beta*Math.Tan(Constants.PiOver2*alpha);
|
|
var factor = Math.Pow(1.0 + (part1*part1), 1.0/(2.0*alpha));
|
var factor1 = Math.Sin(angle)/Math.Pow(Math.Cos(randTheta), 1.0/alpha);
|
var factor2 = Math.Pow(Math.Cos(randTheta - angle)/randW, (1 - alpha)/alpha);
|
|
return location + scale*(factor*factor1*factor2);
|
}
|
else
|
{
|
var part1 = Constants.PiOver2 + (beta*randTheta);
|
var summand = part1*Math.Tan(randTheta);
|
var subtrahend = beta*Math.Log(Constants.PiOver2*randW*Math.Cos(randTheta)/part1);
|
|
return location + scale*Constants.TwoInvPi*(summand - subtrahend);
|
}
|
}
|
|
static void SamplesUnchecked(System.Random rnd, double[] values, double alpha, double beta, double scale, double location)
|
{
|
var randThetas = new double[values.Length];
|
var randWs = new double[values.Length];
|
ContinuousUniform.SamplesUnchecked(rnd, randThetas, -Constants.PiOver2, Constants.PiOver2);
|
Exponential.SamplesUnchecked(rnd, randWs, 1.0);
|
|
if (!1.0.AlmostEqual(alpha))
|
{
|
for (int i = 0; i < values.Length; i++)
|
{
|
var randTheta = randThetas[i];
|
|
var theta = (1.0/alpha)*Math.Atan(beta*Math.Tan(Constants.PiOver2*alpha));
|
var angle = alpha*(randTheta + theta);
|
var part1 = beta*Math.Tan(Constants.PiOver2*alpha);
|
|
var factor = Math.Pow(1.0 + (part1*part1), 1.0/(2.0*alpha));
|
var factor1 = Math.Sin(angle)/Math.Pow(Math.Cos(randTheta), 1.0/alpha);
|
var factor2 = Math.Pow(Math.Cos(randTheta - angle)/randWs[i], (1 - alpha)/alpha);
|
|
values[i] = location + scale*(factor*factor1*factor2);
|
}
|
}
|
else
|
{
|
for (int i = 0; i < values.Length; i++)
|
{
|
var randTheta = randThetas[i];
|
|
var part1 = Constants.PiOver2 + (beta*randTheta);
|
var summand = part1*Math.Tan(randTheta);
|
var subtrahend = beta*Math.Log(Constants.PiOver2*randWs[i]*Math.Cos(randTheta)/part1);
|
|
values[i] = location + scale*Constants.TwoInvPi*(summand - subtrahend);
|
}
|
}
|
}
|
|
static IEnumerable<double> SamplesUnchecked(System.Random rnd, double alpha, double beta, double scale, double location)
|
{
|
while (true)
|
{
|
yield return SampleUnchecked(rnd, alpha, beta, scale, location);
|
}
|
}
|
|
/// <summary>
|
/// Draws a random sample from the distribution.
|
/// </summary>
|
/// <returns>A random number from this distribution.</returns>
|
public double Sample()
|
{
|
return SampleUnchecked(_random, _alpha, _beta, _scale, _location);
|
}
|
|
/// <summary>
|
/// Fills an array with samples generated from the distribution.
|
/// </summary>
|
public void Samples(double[] values)
|
{
|
SamplesUnchecked(_random, values, _alpha, _beta, _scale, _location);
|
}
|
|
/// <summary>
|
/// Generates a sequence of samples from the Stable distribution.
|
/// </summary>
|
/// <returns>a sequence of samples from the distribution.</returns>
|
public IEnumerable<double> Samples()
|
{
|
return SamplesUnchecked(_random, _alpha, _beta, _scale, _location);
|
}
|
|
/// <summary>
|
/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
|
/// </summary>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
/// <param name="x">The location at which to compute the density.</param>
|
/// <returns>the density at <paramref name="x"/>.</returns>
|
/// <seealso cref="Density"/>
|
public static double PDF(double alpha, double beta, double scale, double location, double x)
|
{
|
if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
if (alpha == 2d)
|
{
|
return Normal.PDF(location, Constants.Sqrt2*scale, x);
|
}
|
|
if (alpha == 1d && beta == 0d)
|
{
|
return Cauchy.PDF(location, scale, x);
|
}
|
|
if (alpha == 0.5d && beta == 1d && x >= location)
|
{
|
return (Math.Sqrt(scale/Constants.Pi2)*Math.Exp(-scale/(2*(x - location))))/Math.Pow(x - location, 1.5);
|
}
|
|
throw new NotSupportedException();
|
}
|
|
/// <summary>
|
/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
|
/// </summary>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
/// <param name="x">The location at which to compute the density.</param>
|
/// <returns>the log density at <paramref name="x"/>.</returns>
|
/// <seealso cref="DensityLn"/>
|
public static double PDFLn(double alpha, double beta, double scale, double location, double x)
|
{
|
if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
if (alpha == 2d)
|
{
|
return Normal.PDFLn(location, Constants.Sqrt2*scale, x);
|
}
|
|
if (alpha == 1d && beta == 0d)
|
{
|
return Cauchy.PDFLn(location, scale, x);
|
}
|
|
if (alpha == 0.5d && beta == 1d && x >= location)
|
{
|
return Math.Log(scale/Constants.Pi2)/2 - scale/(2*(x - location)) - 1.5*Math.Log(x - location);
|
}
|
|
throw new NotSupportedException();
|
}
|
|
/// <summary>
|
/// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
|
/// </summary>
|
/// <param name="x">The location at which to compute the cumulative distribution function.</param>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
|
/// <seealso cref="CumulativeDistribution"/>
|
public static double CDF(double alpha, double beta, double scale, double location, double x)
|
{
|
if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
if (alpha == 2d)
|
{
|
return Normal.CDF(location, Constants.Sqrt2*scale, x);
|
}
|
|
if (alpha == 1d && beta == 0d)
|
{
|
return Cauchy.CDF(location, scale, x);
|
}
|
|
if (alpha == 0.5d && beta == 1d)
|
{
|
return SpecialFunctions.Erfc(Math.Sqrt(scale/(2*(x - location))));
|
}
|
|
throw new NotSupportedException();
|
}
|
|
/// <summary>
|
/// Generates a sample from the distribution.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
/// <returns>a sample from the distribution.</returns>
|
public static double Sample(System.Random rnd, double alpha, double beta, double scale, double location)
|
{
|
if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SampleUnchecked(rnd, alpha, beta, scale, location);
|
}
|
|
/// <summary>
|
/// Generates a sequence of samples from the distribution.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
/// <returns>a sequence of samples from the distribution.</returns>
|
public static IEnumerable<double> Samples(System.Random rnd, double alpha, double beta, double scale, double location)
|
{
|
if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SamplesUnchecked(rnd, alpha, beta, scale, location);
|
}
|
|
/// <summary>
|
/// Fills an array with samples generated from the distribution.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="values">The array to fill with the samples.</param>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
/// <returns>a sequence of samples from the distribution.</returns>
|
public static void Samples(System.Random rnd, double[] values, double alpha, double beta, double scale, double location)
|
{
|
if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
SamplesUnchecked(rnd, values, alpha, beta, scale, location);
|
}
|
|
/// <summary>
|
/// Generates a sample from the distribution.
|
/// </summary>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
/// <returns>a sample from the distribution.</returns>
|
public static double Sample(double alpha, double beta, double scale, double location)
|
{
|
if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SampleUnchecked(SystemRandomSource.Default, alpha, beta, scale, location);
|
}
|
|
/// <summary>
|
/// Generates a sequence of samples from the distribution.
|
/// </summary>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
/// <returns>a sequence of samples from the distribution.</returns>
|
public static IEnumerable<double> Samples(double alpha, double beta, double scale, double location)
|
{
|
if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SamplesUnchecked(SystemRandomSource.Default, alpha, beta, scale, location);
|
}
|
|
/// <summary>
|
/// Fills an array with samples generated from the distribution.
|
/// </summary>
|
/// <param name="values">The array to fill with the samples.</param>
|
/// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
|
/// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
|
/// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
|
/// <param name="location">The location (μ) of the distribution.</param>
|
/// <returns>a sequence of samples from the distribution.</returns>
|
public static void Samples(double[] values, double alpha, double beta, double scale, double location)
|
{
|
if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
SamplesUnchecked(SystemRandomSource.Default, values, alpha, beta, scale, location);
|
}
|
}
|
}
|
