forked from tsai/mathnet-numerics
Christoph Ruegg
6 years ago
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3 changed files with 905 additions and 0 deletions
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// <copyright file="LogisticTests.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2016 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System; |
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using System.Linq; |
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using MathNet.Numerics.Distributions; |
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using NUnit.Framework; |
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namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous |
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{ |
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using Random = System.Random; |
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/// <summary>
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/// Logistic distribution tests.
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/// </summary>
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[TestFixture, Category("Distributions")] |
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public class LogisticTests |
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{ |
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/// <summary>
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/// Can create standard logistic.
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/// </summary>
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[Test] |
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public void CanCreateStandardLogistic() |
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{ |
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var l = new Logistic(); |
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Assert.AreEqual(0.0, l.Mean); |
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Assert.AreEqual(1.0, l.Scale); |
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} |
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/// <summary>
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/// Can create logistic.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="scale">Scale parameter value.</param>
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[TestCase(10.0, 0.1)] |
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[TestCase(-5.0, 1.0)] |
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[TestCase(0.0, 10.0)] |
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[TestCase(10.0, 100.0)] |
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[TestCase(-5.0, Double.PositiveInfinity)] |
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public void CanCreateLogistic(double mean, double scale) |
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{ |
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var n = new Logistic(mean, scale); |
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Assert.AreEqual(mean, n.Mean); |
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Assert.AreEqual(scale, n.Scale); |
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} |
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/// <summary>
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/// Logistic create fails with bad parameters.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="scale">Scale parameter value.</param>
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[TestCase(Double.NaN, 1.0)] |
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[TestCase(1.0, Double.NaN)] |
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[TestCase(Double.NaN, Double.NaN)] |
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[TestCase(1.0, -1.0)] |
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public void LogisticCreateFailsWithBadParameters(double mean, double scale) |
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{ |
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Assert.That(() => new Logistic(mean, scale), Throws.ArgumentException); |
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} |
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/// <summary>
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/// Can create logistic from mean and scale parameter value.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="scale">Scale parameter value.</param>
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[TestCase(10.0, 0.1)] |
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[TestCase(-5.0, 1.0)] |
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[TestCase(0.0, 10.0)] |
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[TestCase(10.0, 100.0)] |
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[TestCase(-5.0, Double.PositiveInfinity)] |
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public void CanCreateLogisticFromMeanAndScale(double mean, double scale) |
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{ |
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var n = Logistic.WithMeanScale(mean, scale); |
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Assert.AreEqual(mean, n.Mean); |
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Assert.AreEqual(scale, n.Scale); |
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} |
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/// <summary>
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/// Can create logistic from mean and standard deviation.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="sdev">Standard deviation value.</param>
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[TestCase(10.0, 0.1)] |
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[TestCase(-5.0, 1.0)] |
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[TestCase(0.0, 10.0)] |
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[TestCase(10.0, 100.0)] |
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[TestCase(-5.0, Double.PositiveInfinity)] |
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public void CanCreateLogisticFromMeanAndStdDev(double mean, double sdev) |
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{ |
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var n = Logistic.WithMeanStdDev(mean, sdev); |
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Assert.AreEqual(mean, n.Mean); |
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Assert.AreEqual(sdev, n.StdDev); |
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} |
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/// <summary>
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/// Can create logistic from mean and variance.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="var">Variance value.</param>
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[TestCase(10.0, 0.1)] |
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[TestCase(-5.0, 1.0)] |
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[TestCase(0.0, 10.0)] |
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[TestCase(10.0, 100.0)] |
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[TestCase(-5.0, Double.PositiveInfinity)] |
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public void CanCreateLogisticFromMeanAndVariance(double mean, double var) |
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{ |
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var n = Logistic.WithMeanVariance(mean, var); |
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AssertHelpers.AlmostEqualRelative(mean, n.Mean, 15); |
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AssertHelpers.AlmostEqualRelative(var, n.Variance, 15); |
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} |
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/// <summary>
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/// Can create logistic from mean and precision.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="prec">Precision value.</param>
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[TestCase(10.0, 0.1)] |
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[TestCase(-5.0, 1.0)] |
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[TestCase(0.0, 10.0)] |
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[TestCase(10.0, 100.0)] |
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public void CanCreateLogisticFromMeanAndPrecision(double mean, double prec) |
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{ |
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var n = Logistic.WithMeanPrecision(mean, prec); |
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AssertHelpers.AlmostEqualRelative(mean, n.Mean, 15); |
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AssertHelpers.AlmostEqualRelative(prec, n.Precision, 15); |
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} |
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/// <summary>
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/// Validate ToString.
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/// </summary>
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[Test] |
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public void ValidateToString() |
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{ |
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System.Threading.Thread.CurrentThread.CurrentCulture = System.Globalization.CultureInfo.InvariantCulture; |
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var n = new Logistic(1d, 2d); |
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Assert.AreEqual("Logistic(μ = 1, s = 2)", n.ToString()); |
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} |
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/// <summary>
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/// Validate entropy.
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/// </summary>
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/// <param name="scale">Scale parameter value.</param>
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[TestCase(0.1)] |
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[TestCase(1.0)] |
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[TestCase(10.0)] |
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[TestCase(Double.PositiveInfinity)] |
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public void ValidateEntropy(double scale) |
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{ |
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var n = new Logistic(1.0, scale); |
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Assert.AreEqual(Math.Log(scale) + 2, n.Entropy); |
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} |
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/// <summary>
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/// Validate skewness.
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/// </summary>
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/// <param name="scale">Scale parameter value.</param>
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[TestCase(0.1)] |
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[TestCase(1.0)] |
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[TestCase(10.0)] |
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[TestCase(Double.PositiveInfinity)] |
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public void ValidateSkewness(double scale) |
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{ |
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var n = new Logistic(1.0, scale); |
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Assert.AreEqual(0.0, n.Skewness); |
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} |
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/// <summary>
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/// Validate mean.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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[TestCase(Double.NegativeInfinity)] |
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[TestCase(-0.0)] |
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[TestCase(0.0)] |
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[TestCase(0.1)] |
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[TestCase(1.0)] |
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[TestCase(10.0)] |
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[TestCase(Double.PositiveInfinity)] |
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public void ValidateMode(double mean) |
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{ |
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var n = new Logistic(mean, 1.0); |
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Assert.AreEqual(mean, n.Mode); |
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} |
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/// <summary>
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/// Validate median.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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[TestCase(Double.NegativeInfinity)] |
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[TestCase(-0.0)] |
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[TestCase(0.0)] |
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[TestCase(0.1)] |
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[TestCase(1.0)] |
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[TestCase(10.0)] |
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[TestCase(Double.PositiveInfinity)] |
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public void ValidateMedian(double mean) |
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{ |
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var n = new Logistic(mean, 1.0); |
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Assert.AreEqual(mean, n.Median); |
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} |
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/// <summary>
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/// Validate minimum.
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/// </summary>
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[Test] |
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public void ValidateMinimum() |
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{ |
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var n = new Logistic(); |
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Assert.AreEqual(Double.NegativeInfinity, n.Minimum); |
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} |
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/// <summary>
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/// Validate maximum.
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/// </summary>
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[Test] |
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public void ValidateMaximum() |
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{ |
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var n = new Logistic(); |
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Assert.AreEqual(Double.PositiveInfinity, n.Maximum); |
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} |
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/// <summary>
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/// Can sample static.
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/// </summary>
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[Test] |
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public void CanSampleStatic() |
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{ |
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Logistic.Sample(new Random(0), 0.0, 1.0); |
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} |
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/// <summary>
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/// Can sample sequence static.
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/// </summary>
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[Test] |
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public void CanSampleSequenceStatic() |
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{ |
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var ied = Logistic.Samples(new Random(0), 0.0, 1.0); |
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GC.KeepAlive(ied.Take(5).ToArray()); |
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} |
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/// <summary>
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/// Fail sample static with bad parameters.
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/// </summary>
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[Test] |
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public void FailSampleStatic() |
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{ |
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Assert.That(() => { var d = Logistic.Sample(new Random(0), 0.0, -1.0); }, Throws.ArgumentException); |
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} |
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/// <summary>
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/// Fail sample sequence static with bad parameters.
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/// </summary>
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[Test] |
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public void FailSampleSequenceStatic() |
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{ |
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Assert.That(() => { var ied = Logistic.Samples(new Random(0), 0.0, -1.0).First(); }, Throws.ArgumentException); |
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} |
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/// <summary>
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/// Can sample.
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/// </summary>
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[Test] |
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public void CanSample() |
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{ |
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var n = new Logistic(); |
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n.Sample(); |
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} |
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/// <summary>
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/// Can sample sequence.
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/// </summary>
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[Test] |
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public void CanSampleSequence() |
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{ |
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var n = new Logistic(); |
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var ied = n.Samples(); |
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GC.KeepAlive(ied.Take(5).ToArray()); |
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} |
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/// <summary>
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/// Validate density.
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/// </summary>
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/// <param name="x">Input X value.</param>
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/// <param name="d">Expected value.</param>
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[TestCase(Double.NegativeInfinity, double.NaN)] |
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[TestCase(-5.0, 0.00332402833539508)] |
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[TestCase(-2.0, 0.01422651193986778)] |
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[TestCase(0.0, 0.03505185827255409)] |
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[TestCase(4.0, 0.11750185610079725)] |
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[TestCase(5.0, 0.12500000000000000)] |
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[TestCase(6.0, 0.11750185610079725)] |
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[TestCase(10.0, 0.03505185827255409)] |
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[TestCase(Double.PositiveInfinity, 0)] |
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public void ValidateDensity(double x, double d) |
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{ |
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var n = Logistic.WithMeanScale(5.0, 2.0); |
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AssertHelpers.AlmostEqualRelative(d, n.Density(x), 9); |
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AssertHelpers.AlmostEqualRelative(d, Logistic.PDF(5.0, 2.0, x), 9); |
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} |
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/// <summary>
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/// Validate density.
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/// </summary>
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/// <param name="x">Input X value.</param>
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/// <param name="d">Expected value.</param>
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[TestCase(Double.NegativeInfinity, double.NaN)] |
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[TestCase(-5.0, -5.70657787753818)] |
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[TestCase(-2.0, -4.25264801710519)] |
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[TestCase(0.0, -3.35092664914504)] |
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[TestCase(4.0, -2.14130114892016)] |
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[TestCase(5.0, -2.07944154167984)] |
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[TestCase(6.0, -2.14130114892016)] |
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[TestCase(10.0, -3.35092664914504)] |
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[TestCase(Double.PositiveInfinity, Double.NegativeInfinity)] |
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public void ValidateLogDensity(double x, double d) |
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{ |
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var n = Logistic.WithMeanScale(5.0, 2.0); |
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AssertHelpers.AlmostEqualRelative(d, n.DensityLn(x), 9); |
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AssertHelpers.AlmostEqualRelative(d, Logistic.PDFLn(5.0, 2.0, x), 9); |
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} |
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/// <summary>
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/// Validate cumulative distribution.
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/// </summary>
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/// <param name="x">Input X value.</param>
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/// <param name="p">Expected value.</param>
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[TestCase(Double.NegativeInfinity, 0.0)] |
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[TestCase(-5.0, 0.00669285092428486)] |
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[TestCase(-2.0, 0.0293122307513563)] |
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[TestCase(0.0, 0.0758581800212435)] |
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[TestCase(4.0, 0.377540668798145)] |
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[TestCase(5.0, 0.5)] |
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[TestCase(6.0, 0.622459331201855)] |
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[TestCase(10.0, 0.924141819978757)] |
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[TestCase(Double.PositiveInfinity, 1.0)] |
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public void ValidateCumulativeDistribution(double x, double p) |
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{ |
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var n = Logistic.WithMeanScale(5.0, 2.0); |
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AssertHelpers.AlmostEqualRelative(p, n.CumulativeDistribution(x), 9); |
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AssertHelpers.AlmostEqualRelative(p, Logistic.CDF(5.0, 2.0, x), 9); |
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} |
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/// <summary>
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/// Validate inverse cumulative distribution.
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/// </summary>
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/// <param name="x">Input X value.</param>
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/// <param name="p">Expected value.</param>
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[TestCase(Double.NegativeInfinity, 0.0)] |
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[TestCase(-5.0, 0.00669285092428486)] |
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[TestCase(-2.0, 0.0293122307513563)] |
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[TestCase(0.0, 0.0758581800212435)] |
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[TestCase(4.0, 0.377540668798145)] |
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[TestCase(5.0, 0.5)] |
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[TestCase(6.0, 0.622459331201855)] |
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[TestCase(10.0, 0.924141819978757)] |
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[TestCase(Double.PositiveInfinity, 1.0)] |
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public void ValidateInverseCumulativeDistribution(double x, double p) |
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{ |
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var n = Logistic.WithMeanScale(5.0, 2.0); |
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AssertHelpers.AlmostEqualRelative(x, n.InverseCumulativeDistribution(p), 14); |
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AssertHelpers.AlmostEqualRelative(x, Logistic.InvCDF(5.0, 2.0, p), 14); |
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} |
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} |
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} |
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@ -0,0 +1,514 @@ |
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// <copyright file="Logistic.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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||||
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//
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// Copyright (c) 2009-2015 Math.NET
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//
|
||||
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// 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.Random; |
||||
|
using MathNet.Numerics.Statistics; |
||||
|
|
||||
|
namespace MathNet.Numerics.Distributions |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Continuous Univariate Logistic distribution.
|
||||
|
/// For details about this distribution, see
|
||||
|
/// <a href="http://en.wikipedia.org/wiki/Logistic_distribution">Wikipedia - Logistic distribution</a>.
|
||||
|
/// </summary>
|
||||
|
public class Logistic : IContinuousDistribution |
||||
|
{ |
||||
|
System.Random _random; |
||||
|
|
||||
|
readonly double _mean; |
||||
|
readonly double _scale; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Initializes a new instance of the Logistic class. This is a logistic distribution with mean 0.0
|
||||
|
/// and scale 1.0. The distribution will be initialized with the default <seealso cref="System.Random"/>
|
||||
|
/// random number generator.
|
||||
|
/// </summary>
|
||||
|
public Logistic() |
||||
|
: this(0.0, 1.0) |
||||
|
{ |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Initializes a new instance of the Logistic class. This is a logistic distribution with mean 0.0
|
||||
|
/// and scale 1.0. The distribution will be initialized with the default <seealso cref="System.Random"/>
|
||||
|
/// random number generator.
|
||||
|
/// </summary>
|
||||
|
/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
|
||||
|
public Logistic(System.Random randomSource) |
||||
|
: this(0.0, 1.0, randomSource) |
||||
|
{ |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Initializes a new instance of the Logistic class with a particular mean and scale parameter. The
|
||||
|
/// distribution will be initialized with the default <seealso cref="System.Random"/> random number generator.
|
||||
|
/// </summary>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
public Logistic(double mean, double scale) |
||||
|
{ |
||||
|
if (!IsValidParameterSet(mean, scale)) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
|
||||
|
_random = SystemRandomSource.Default; |
||||
|
_mean = mean; |
||||
|
_scale = scale; |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Initializes a new instance of the Logistic class with a particular mean and standard deviation. The distribution will
|
||||
|
/// be initialized with the default <seealso cref="System.Random"/> random number generator.
|
||||
|
/// </summary>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
|
||||
|
public Logistic(double mean, double scale, System.Random randomSource) |
||||
|
{ |
||||
|
if (!IsValidParameterSet(mean, scale)) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
|
||||
|
_random = randomSource ?? SystemRandomSource.Default; |
||||
|
_mean = mean; |
||||
|
_scale = scale; |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Constructs a logistic distribution from a mean and scale parameter.
|
||||
|
/// </summary>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
/// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
|
||||
|
/// <returns>a logistic distribution.</returns>
|
||||
|
public static Logistic WithMeanScale(double mean, double scale, System.Random randomSource = null) |
||||
|
{ |
||||
|
return new Logistic(mean, scale, randomSource); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Constructs a logistic distribution from a mean and standard deviation.
|
||||
|
/// </summary>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="stddev">The standard deviation (σ) of the logistic distribution. Range: σ > 0.</param>
|
||||
|
/// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
|
||||
|
/// <returns>a logistic distribution.</returns>
|
||||
|
public static Logistic WithMeanStdDev(double mean, double stddev, System.Random randomSource = null) |
||||
|
{ |
||||
|
var scale = Math.Sqrt(3) * stddev / Math.PI; |
||||
|
return new Logistic(mean, scale, randomSource); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Constructs a logistic distribution from a mean and variance.
|
||||
|
/// </summary>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="var">The variance (σ^2) of the logistic distribution. Range: (σ^2) > 0.</param>
|
||||
|
/// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
|
||||
|
/// <returns>A logistic distribution.</returns>
|
||||
|
public static Logistic WithMeanVariance(double mean, double var, System.Random randomSource = null) |
||||
|
{ |
||||
|
return WithMeanStdDev(mean, Math.Sqrt(var), randomSource); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Constructs a logistic distribution from a mean and precision.
|
||||
|
/// </summary>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="precision">The precision of the logistic distribution. Range: precision > 0.</param>
|
||||
|
/// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
|
||||
|
/// <returns>A logistic distribution.</returns>
|
||||
|
public static Logistic WithMeanPrecision(double mean, double precision, System.Random randomSource = null) |
||||
|
{ |
||||
|
return WithMeanVariance(mean, 1 / precision, randomSource); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// A string representation of the distribution.
|
||||
|
/// </summary>
|
||||
|
/// <returns>a string representation of the distribution.</returns>
|
||||
|
public override string ToString() |
||||
|
{ |
||||
|
return $"Logistic(μ = {_mean}, s = {_scale})"; |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Tests whether the provided values are valid parameters for this distribution.
|
||||
|
/// </summary>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
public static bool IsValidParameterSet(double mean, double scale) |
||||
|
{ |
||||
|
return scale > 0.0 && !double.IsNaN(mean); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the scale parameter of the Logistic distribution. Range: s > 0.
|
||||
|
/// </summary>
|
||||
|
public double Scale => _scale; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the mean (μ) of the logistic distribution.
|
||||
|
/// </summary>
|
||||
|
public double Mean => _mean; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the standard deviation (σ) of the logistic distribution. Range: σ > 0.
|
||||
|
/// </summary>
|
||||
|
public double StdDev => Math.Sqrt(Variance); |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the variance of the logistic distribution.
|
||||
|
/// </summary>
|
||||
|
public double Variance => (Math.Pow(_scale, 2) * Math.Pow(Math.PI,2))/3; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the precision of the logistic distribution.
|
||||
|
/// </summary>
|
||||
|
public double Precision => 1.0/Variance; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets 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 entropy of the logistic distribution.
|
||||
|
/// </summary>
|
||||
|
public double Entropy => Math.Log(_scale) + 2; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the skewness of the logistic distribution.
|
||||
|
/// </summary>
|
||||
|
public double Skewness => 0.0; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the mode of the logistic distribution.
|
||||
|
/// </summary>
|
||||
|
public double Mode => _mean; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the median of the logistic distribution.
|
||||
|
/// </summary>
|
||||
|
public double Median => _mean; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the minimum of the logistic distribution.
|
||||
|
/// </summary>
|
||||
|
public double Minimum => double.NegativeInfinity; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the maximum of the logistic 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>
|
||||
|
/// <seealso cref="PDF"/>
|
||||
|
public double Density(double x) |
||||
|
{ |
||||
|
return PDF(_mean, _scale, 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(_mean, _scale, 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(_mean, _scale, 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(_mean, _scale, p); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Generates a sample from the logistic distribution using the <i>Box-Muller</i> algorithm.
|
||||
|
/// </summary>
|
||||
|
/// <returns>a sample from the distribution.</returns>
|
||||
|
public double Sample() |
||||
|
{ |
||||
|
return SampleUnchecked(_random, _mean, _scale); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Fills an array with samples generated from the distribution.
|
||||
|
/// </summary>
|
||||
|
public void Samples(double[] values) |
||||
|
{ |
||||
|
SamplesUnchecked(_random, values, _mean, _scale); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Generates a sequence of samples from the logistic distribution using the <i>Box-Muller</i> algorithm.
|
||||
|
/// </summary>
|
||||
|
/// <returns>a sequence of samples from the distribution.</returns>
|
||||
|
public IEnumerable<double> Samples() |
||||
|
{ |
||||
|
return SamplesUnchecked(_random, _mean, _scale); |
||||
|
} |
||||
|
|
||||
|
internal static double SampleUnchecked(System.Random rnd, double mean, double scale) |
||||
|
{ |
||||
|
return InvCDF(mean, scale, rnd.NextDouble()); |
||||
|
} |
||||
|
|
||||
|
internal static IEnumerable<double> SamplesUnchecked(System.Random rnd, double mean, double scale) |
||||
|
{ |
||||
|
while (true) |
||||
|
{ |
||||
|
yield return InvCDF(mean, scale, rnd.NextDouble()); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
internal static void SamplesUnchecked(System.Random rnd, double[] values, double mean, double scale) |
||||
|
{ |
||||
|
if (values.Length == 0) |
||||
|
{ |
||||
|
return; |
||||
|
} |
||||
|
|
||||
|
for (int i = 0; i < values.Length; i++) |
||||
|
{ |
||||
|
values[i] = SampleUnchecked(rnd, mean, scale); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
|
||||
|
/// </summary>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</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 mean, double scale, double x) |
||||
|
{ |
||||
|
if (scale <= 0.0) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
|
||||
|
var z = (x - mean)/scale; |
||||
|
return Math.Exp(-z) / (scale * Math.Pow(1.0 + Math.Exp(-z), 2)); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
|
||||
|
/// </summary>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</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 mean, double scale, double x) |
||||
|
{ |
||||
|
if (scale <= 0.0) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
|
||||
|
var z = (x - mean)/scale; |
||||
|
return -z - Math.Log(scale) - (2 * Math.Log(1+Math.Exp(-z))); |
||||
|
} |
||||
|
|
||||
|
/// <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="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
|
||||
|
/// <seealso cref="CumulativeDistribution"/>
|
||||
|
/// <remarks>MATLAB: normcdf</remarks>
|
||||
|
public static double CDF(double mean, double scale, double x) |
||||
|
{ |
||||
|
if (scale <= 0.0) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
var z = (x - mean)/scale; |
||||
|
return 1 / (1 + Math.Exp(-z)); |
||||
|
} |
||||
|
|
||||
|
/// <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="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
/// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
|
||||
|
/// <seealso cref="InverseCumulativeDistribution"/>
|
||||
|
/// <remarks>MATLAB: norminv</remarks>
|
||||
|
public static double InvCDF(double mean, double scale, double p) |
||||
|
{ |
||||
|
if (scale <= 0.0) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
|
||||
|
return mean + (scale*Math.Log(p / (1-p))); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Generates a sample from the logistic distribution using the <i>Box-Muller</i> algorithm.
|
||||
|
/// </summary>
|
||||
|
/// <param name="rnd">The random number generator to use.</param>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
/// <returns>a sample from the distribution.</returns>
|
||||
|
public static double Sample(System.Random rnd, double mean, double scale) |
||||
|
{ |
||||
|
if (scale <= 0.0) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
|
||||
|
return SampleUnchecked(rnd, mean, scale); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Generates a sequence of samples from the logistic distribution using the <i>Box-Muller</i> algorithm.
|
||||
|
/// </summary>
|
||||
|
/// <param name="rnd">The random number generator to use.</param>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
/// <returns>a sequence of samples from the distribution.</returns>
|
||||
|
public static IEnumerable<double> Samples(System.Random rnd, double mean, double scale) |
||||
|
{ |
||||
|
if (scale <= 0.0) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
|
||||
|
return SamplesUnchecked(rnd, mean, scale); |
||||
|
} |
||||
|
|
||||
|
/// <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="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
/// <returns>a sequence of samples from the distribution.</returns>
|
||||
|
public static void Samples(System.Random rnd, double[] values, double mean, double scale) |
||||
|
{ |
||||
|
if (scale <= 0.0) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
|
||||
|
SamplesUnchecked(rnd, values, mean, scale); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Generates a sample from the logistic distribution using the <i>Box-Muller</i> algorithm.
|
||||
|
/// </summary>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
/// <returns>a sample from the distribution.</returns>
|
||||
|
public static double Sample(double mean, double scale) |
||||
|
{ |
||||
|
if (scale <= 0.0) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
|
||||
|
return SampleUnchecked(SystemRandomSource.Default, mean, scale); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Generates a sequence of samples from the logistic distribution using the <i>Box-Muller</i> algorithm.
|
||||
|
/// </summary>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
/// <returns>a sequence of samples from the distribution.</returns>
|
||||
|
public static IEnumerable<double> Samples(double mean, double scale) |
||||
|
{ |
||||
|
if (scale <= 0.0) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
|
||||
|
return SamplesUnchecked(SystemRandomSource.Default, mean, scale); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Fills an array with samples generated from the distribution.
|
||||
|
/// </summary>
|
||||
|
/// <param name="values">The array to fill with the samples.</param>
|
||||
|
/// <param name="mean">The mean (μ) of the logistic distribution.</param>
|
||||
|
/// <param name="scale">The scale (s) of the logistic distribution. Range: s > 0.</param>
|
||||
|
/// <returns>a sequence of samples from the distribution.</returns>
|
||||
|
public static void Samples(double[] values, double mean, double scale) |
||||
|
{ |
||||
|
if (scale <= 0.0) |
||||
|
{ |
||||
|
throw new ArgumentException("Invalid parametrization for the distribution."); |
||||
|
} |
||||
|
|
||||
|
SamplesUnchecked(SystemRandomSource.Default, values, mean, scale); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
Loading…
Reference in new issue