forked from tsai/mathnet-numerics
Christoph Ruegg
13 years ago
5 changed files with 568 additions and 0 deletions
@ -0,0 +1,145 @@ |
|||||
|
// <copyright file="ContinuousUniformDistribution.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 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 MathNet.Numerics.Distributions; |
||||
|
|
||||
|
namespace Examples.TriangularExamples |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// ContinuousUniform distribution example
|
||||
|
/// </summary>
|
||||
|
public class TriangularDistribution : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/ref/TriangularDistribution.html"/>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Triangular distribution"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Triangular distribution properties and samples generating examples"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
/// <a href="https://en.wikipedia.org/wiki/Triangular_distribution">Triangular distribution</a>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// 1. Initialize
|
||||
|
var triangular = new Triangular(0, 1, 0.3); |
||||
|
Console.WriteLine(@"1. Initialize the new instance of the Triangular distribution class with parameters Lower = {0}, Upper = {1}, Mode = {2}", triangular.LowerBound, triangular.UpperBound, triangular.Mode); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Distributuion properties:
|
||||
|
Console.WriteLine(@"2. {0} distributuion properties:", triangular); |
||||
|
|
||||
|
// Cumulative distribution function
|
||||
|
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", triangular.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000")); |
||||
|
|
||||
|
// Probability density
|
||||
|
Console.WriteLine(@"{0} - Probability density at location '0.3'", triangular.Density(0.3).ToString(" #0.00000;-#0.00000")); |
||||
|
|
||||
|
// Log probability density
|
||||
|
Console.WriteLine(@"{0} - Log probability density at location '0.3'", triangular.DensityLn(0.3).ToString(" #0.00000;-#0.00000")); |
||||
|
|
||||
|
// Entropy
|
||||
|
Console.WriteLine(@"{0} - Entropy", triangular.Entropy.ToString(" #0.00000;-#0.00000")); |
||||
|
|
||||
|
// Largest element in the domain
|
||||
|
Console.WriteLine(@"{0} - Largest element in the domain", triangular.Maximum.ToString(" #0.00000;-#0.00000")); |
||||
|
|
||||
|
// Smallest element in the domain
|
||||
|
Console.WriteLine(@"{0} - Smallest element in the domain", triangular.Minimum.ToString(" #0.00000;-#0.00000")); |
||||
|
|
||||
|
// Mean
|
||||
|
Console.WriteLine(@"{0} - Mean", triangular.Mean.ToString(" #0.00000;-#0.00000")); |
||||
|
|
||||
|
// Median
|
||||
|
Console.WriteLine(@"{0} - Median", triangular.Median.ToString(" #0.00000;-#0.00000")); |
||||
|
|
||||
|
// Mode
|
||||
|
Console.WriteLine(@"{0} - Mode", triangular.Mode.ToString(" #0.00000;-#0.00000")); |
||||
|
|
||||
|
// Variance
|
||||
|
Console.WriteLine(@"{0} - Variance", triangular.Variance.ToString(" #0.00000;-#0.00000")); |
||||
|
|
||||
|
// Standard deviation
|
||||
|
Console.WriteLine(@"{0} - Standard deviation", triangular.StdDev.ToString(" #0.00000;-#0.00000")); |
||||
|
|
||||
|
// Skewness
|
||||
|
Console.WriteLine(@"{0} - Skewness", triangular.Skewness.ToString(" #0.00000;-#0.00000")); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 10 samples
|
||||
|
Console.WriteLine(@"3. Generate 10 samples of the Triangular distribution"); |
||||
|
for (var i = 0; i < 10; i++) |
||||
|
{ |
||||
|
Console.Write(triangular.Sample().ToString("N05") + @" "); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 10000 samples with starting parameters
|
||||
|
Console.WriteLine(@"4. Generate 100000 samples of the Triangular({0}, {1}, {2}) distribution and display histogram", triangular.LowerBound, triangular.UpperBound, triangular.Mode); |
||||
|
var data = new double[100000]; |
||||
|
for (var i = 0; i < data.Length; i++) |
||||
|
{ |
||||
|
data[i] = triangular.Sample(); |
||||
|
} |
||||
|
|
||||
|
ConsoleHelper.DisplayHistogram(data); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 10000 with different parameters
|
||||
|
triangular.UpperBound = 10; |
||||
|
triangular.Mode = 8; |
||||
|
triangular.LowerBound = 2; |
||||
|
Console.WriteLine(@"4. Generate 100000 samples of the Triangular({0}, {1}, {2}) distribution and display histogram", triangular.LowerBound, triangular.UpperBound, triangular.Mode); |
||||
|
for (var i = 0; i < data.Length; i++) |
||||
|
{ |
||||
|
data[i] = triangular.Sample(); |
||||
|
} |
||||
|
|
||||
|
ConsoleHelper.DisplayHistogram(data); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,420 @@ |
|||||
|
// <copyright file="TriangularUniform.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
//
|
||||
|
// 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 MathNet.Numerics.Properties; |
||||
|
using MathNet.Numerics.Random; |
||||
|
|
||||
|
namespace MathNet.Numerics.Distributions |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Triangular distribution.
|
||||
|
/// For details, see <a href="https://en.wikipedia.org/wiki/Triangular_distribution">Wikipedia - Triangular distribution</a>.
|
||||
|
/// </summary>
|
||||
|
/// <remarks><para>The distribution will use the <see cref="System.Random"/> by default.
|
||||
|
/// Users can get/set the random number generator by using the <see cref="RandomSource"/> property.</para>
|
||||
|
/// <para>The statistics classes will check whether all the incoming parameters are in the allowed range. This might involve heavy computation. Optionally, by setting Control.CheckDistributionParameters
|
||||
|
/// to <c>false</c>, all parameter checks can be turned off.</para></remarks>
|
||||
|
public class Triangular : IContinuousDistribution |
||||
|
{ |
||||
|
System.Random _random; |
||||
|
|
||||
|
double _lower; |
||||
|
double _upper; |
||||
|
double _mode; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Initializes a new instance of the Triangular class with the given lower bound, upper bound and mode.
|
||||
|
/// </summary>
|
||||
|
/// <param name="lower">Lower bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="upper">Upper bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="mode">Mode (most frequent value). Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <exception cref="ArgumentException">If the upper bound is smaller than the mode or if the mode is smaller than the lower bound.</exception>
|
||||
|
public Triangular(double lower, double upper, double mode) |
||||
|
{ |
||||
|
_random = MersenneTwister.Default; |
||||
|
SetParameters(lower, upper, mode); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Initializes a new instance of the Triangular class with the given lower bound, upper bound and mode.
|
||||
|
/// </summary>
|
||||
|
/// <param name="lower">Lower bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="upper">Upper bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="mode">Mode (most frequent value). Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
|
||||
|
/// <exception cref="ArgumentException">If the upper bound is smaller than the mode or if the mode is smaller than the lower bound.</exception>
|
||||
|
public Triangular(double lower, double upper, double mode, System.Random randomSource) |
||||
|
{ |
||||
|
_random = randomSource ?? MersenneTwister.Default; |
||||
|
SetParameters(lower, upper, mode); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// A string representation of the distribution.
|
||||
|
/// </summary>
|
||||
|
/// <returns>a string representation of the distribution.</returns>
|
||||
|
public override string ToString() |
||||
|
{ |
||||
|
return "Triangular(Lower = " + _lower + ", Upper = " + _upper + ", Mode = " + _mode + ")"; |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Sets the parameters of the distribution after checking their validity.
|
||||
|
/// </summary>
|
||||
|
/// <param name="lower">Lower bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="upper">Upper bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="mode">Mode (most frequent value). Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
|
||||
|
void SetParameters(double lower, double upper, double mode) |
||||
|
{ |
||||
|
if (upper < mode || mode < lower || Double.IsNaN(upper) || Double.IsNaN(lower) || Double.IsNaN(mode)) |
||||
|
{ |
||||
|
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters); |
||||
|
} |
||||
|
|
||||
|
_lower = lower; |
||||
|
_upper = upper; |
||||
|
_mode = mode; |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets or sets the lower bound of the distribution.
|
||||
|
/// </summary>
|
||||
|
public double LowerBound |
||||
|
{ |
||||
|
get { return _lower; } |
||||
|
set { SetParameters(value, _upper, _mode); } |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets or sets the upper bound of the distribution.
|
||||
|
/// </summary>
|
||||
|
public double UpperBound |
||||
|
{ |
||||
|
get { return _upper; } |
||||
|
set { SetParameters(_lower, value, _mode); } |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets or sets the random number generator which is used to draw random samples.
|
||||
|
/// </summary>
|
||||
|
public System.Random RandomSource |
||||
|
{ |
||||
|
get { return _random; } |
||||
|
set { _random = value ?? MersenneTwister.Default; } |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the mean of the distribution.
|
||||
|
/// </summary>
|
||||
|
public double Mean |
||||
|
{ |
||||
|
get { return (_lower + _upper + _mode) / 3.0; } |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the variance of the distribution.
|
||||
|
/// </summary>
|
||||
|
public double Variance |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
var a = _lower; |
||||
|
var b = _upper; |
||||
|
var c = _mode; |
||||
|
return (a * a + b * b + c * c - a * b - a * c - b * c) / 18.0; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the standard deviation of the distribution.
|
||||
|
/// </summary>
|
||||
|
public double StdDev |
||||
|
{ |
||||
|
get { return Math.Sqrt(Variance); } |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the entropy of the distribution.
|
||||
|
/// </summary>
|
||||
|
/// <value></value>
|
||||
|
public double Entropy |
||||
|
{ |
||||
|
get { return 0.5 + Math.Log((_upper - _lower) / 2); } |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the skewness of the distribution.
|
||||
|
/// </summary>
|
||||
|
public double Skewness |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
var a = _lower; |
||||
|
var b = _upper; |
||||
|
var c = _mode; |
||||
|
var q = Math.Sqrt(2) * (a + b - 2 * c) * (2 * a - b - c) * (a - 2 * b + c); |
||||
|
var d = 5 * Math.Pow(a * a + b * b + c * c - a * b - a * c - b * c, 3.0 / 2); |
||||
|
return q / d; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets or sets the mode of the distribution.
|
||||
|
/// </summary>
|
||||
|
public double Mode |
||||
|
{ |
||||
|
get { return _mode; } |
||||
|
set { SetParameters(_lower, _upper, value); } |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the median of the distribution.
|
||||
|
/// </summary>
|
||||
|
/// <value></value>
|
||||
|
public double Median |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
var a = _lower; |
||||
|
var b = _upper; |
||||
|
var c = _mode; |
||||
|
return c >= (a + b) / 2 |
||||
|
? a + Math.Sqrt((b - a) * (c - a) / 2) |
||||
|
: b - Math.Sqrt((b - a) * (b - c) / 2); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the minimum of the distribution.
|
||||
|
/// </summary>
|
||||
|
public double Minimum |
||||
|
{ |
||||
|
get { return _lower; } |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the maximum of the distribution.
|
||||
|
/// </summary>
|
||||
|
public double Maximum |
||||
|
{ |
||||
|
get { return _upper; } |
||||
|
} |
||||
|
|
||||
|
/// <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>
|
||||
|
/// <seealso cref="PDF"/>
|
||||
|
public double Density(double x) |
||||
|
{ |
||||
|
return PDF(_lower, _upper, _mode, 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>
|
||||
|
/// <seealso cref="PDFLn"/>
|
||||
|
public double DensityLn(double x) |
||||
|
{ |
||||
|
return PDFLn(_lower, _upper, _mode, 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>
|
||||
|
/// <seealso cref="CDF"/>
|
||||
|
public double CumulativeDistribution(double x) |
||||
|
{ |
||||
|
return CDF(_lower, _upper, _mode, x); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
|
||||
|
/// at the given probability. This is also known as the quantile or percent point function.
|
||||
|
/// </summary>
|
||||
|
/// <param name="p">The location at which to compute the inverse cumulative density.</param>
|
||||
|
/// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
|
||||
|
/// <seealso cref="InvCDF"/>
|
||||
|
public double InverseCumulativeDistribution(double p) |
||||
|
{ |
||||
|
return InvCDF(_lower, _upper, _mode, p); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Generates a sample from the <c>Triangular</c> distribution.
|
||||
|
/// </summary>
|
||||
|
/// <returns>a sample from the distribution.</returns>
|
||||
|
public double Sample() |
||||
|
{ |
||||
|
return Sample(_random, _lower, _upper, _mode); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Generates a sequence of samples from the <c>Triangular</c> distribution.
|
||||
|
/// </summary>
|
||||
|
/// <returns>a sequence of samples from the distribution.</returns>
|
||||
|
public IEnumerable<double> Samples() |
||||
|
{ |
||||
|
return Samples(_random, _lower, _upper, _mode); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
|
||||
|
/// </summary>
|
||||
|
/// <param name="lower">Lower bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="upper">Upper bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="mode">Mode (most frequent value). Range: lower ≤ mode ≤ upper</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 lower, double upper, double mode, double x) |
||||
|
{ |
||||
|
if (upper < mode) throw new ArgumentOutOfRangeException("upper", Resources.InvalidDistributionParameters); |
||||
|
if (mode < lower) throw new ArgumentOutOfRangeException("lower", Resources.InvalidDistributionParameters); // TODO: Is "lower" the appropriate argument here?
|
||||
|
|
||||
|
var a = lower; |
||||
|
var b = upper; |
||||
|
var c = mode; |
||||
|
|
||||
|
if (a <= x && x <= c) return 2 * (x - a) / ((b - a) * (c - a)); |
||||
|
if (c < x & x <= b) return 2 * (b - x) / ((b - a) * (b - c)); |
||||
|
return 0; |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
|
||||
|
/// </summary>
|
||||
|
/// <param name="lower">Lower bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="upper">Upper bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="mode">Mode (most frequent value). Range: lower ≤ mode ≤ upper</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 lower, double upper, double mode, double x) |
||||
|
{ |
||||
|
return Math.Log(PDF(lower, upper, mode, 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>
|
||||
|
/// <param name="lower">Lower bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="upper">Upper bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="mode">Mode (most frequent value). Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
|
||||
|
/// <seealso cref="CumulativeDistribution"/>
|
||||
|
public static double CDF(double lower, double upper, double mode, double x) |
||||
|
{ |
||||
|
if (upper < mode) throw new ArgumentOutOfRangeException("upper", Resources.InvalidDistributionParameters); |
||||
|
if (mode < lower) throw new ArgumentOutOfRangeException("lower", Resources.InvalidDistributionParameters); // TODO: Is "lower" the appropriate argument here?
|
||||
|
|
||||
|
var a = lower; |
||||
|
var b = upper; |
||||
|
var c = mode; |
||||
|
|
||||
|
if (x < a) return 0; |
||||
|
if (a <= x && x <= c) return (x - a) * (x - a) / ((b - a) * (c - a)); |
||||
|
if (c < x & x <= b) return 1 - (b - x) * (b - x) / ((b - a) * (b - c)); |
||||
|
return 1; |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
|
||||
|
/// at the given probability. This is also known as the quantile or percent point function.
|
||||
|
/// </summary>
|
||||
|
/// <param name="p">The location at which to compute the inverse cumulative density.</param>
|
||||
|
/// <param name="lower">Lower bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="upper">Upper bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="mode">Mode (most frequent value). Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
|
||||
|
/// <seealso cref="InverseCumulativeDistribution"/>
|
||||
|
public static double InvCDF(double lower, double upper, double mode, double p) |
||||
|
{ |
||||
|
if (upper < mode) throw new ArgumentOutOfRangeException("upper", Resources.InvalidDistributionParameters); |
||||
|
if (mode < lower) throw new ArgumentOutOfRangeException("lower", Resources.InvalidDistributionParameters); // TODO: Is "lower" the appropriate argument here?
|
||||
|
|
||||
|
var a = lower; |
||||
|
var b = upper; |
||||
|
var c = mode; |
||||
|
|
||||
|
if (p <= 0) return lower; |
||||
|
// Taken from http://www.ntrand.com/triangular-distribution/
|
||||
|
if (p < (c - a) / (b - a)) return a + Math.Sqrt(p * (c - a) * (b - a)); |
||||
|
if (p < 1) return b - Math.Sqrt((1 - p) * (b - c) * (b - a)); |
||||
|
return upper; |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Generates a sample from the <c>Triangular</c> distribution.
|
||||
|
/// </summary>
|
||||
|
/// <param name="rnd">The random number generator to use.</param>
|
||||
|
/// <param name="lower">Lower bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="upper">Upper bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="mode">Mode (most frequent value). Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <returns>a sample from the distribution.</returns>
|
||||
|
public double Sample(System.Random rnd, double lower, double upper, double mode) |
||||
|
{ |
||||
|
var a = lower; |
||||
|
var b = upper; |
||||
|
var c = mode; |
||||
|
var u = rnd.NextDouble(); |
||||
|
|
||||
|
return u < (c - a) / (b - a) |
||||
|
? a + Math.Sqrt(u * (b - a) * (c - a)) |
||||
|
: b - Math.Sqrt((1 - u) * (b - a) * (b - c)); ; |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Generates a sequence of samples from the <c>Triangular</c> distribution.
|
||||
|
/// </summary>
|
||||
|
/// <param name="rnd">The random number generator to use.</param>
|
||||
|
/// <param name="lower">Lower bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="upper">Upper bound. Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <param name="mode">Mode (most frequent value). Range: lower ≤ mode ≤ upper</param>
|
||||
|
/// <returns>a sequence of samples from the distribution.</returns>
|
||||
|
public IEnumerable<double> Samples(System.Random rnd, double lower, double upper, double mode) |
||||
|
{ |
||||
|
while (true) |
||||
|
{ |
||||
|
yield return Sample(rnd, lower, upper, mode); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
} |
||||
|
} |
||||
Loading…
Reference in new issue