diff --git a/src/Numerics.Tests/DistributionTests/CommonDistributionTests.cs b/src/Numerics.Tests/DistributionTests/CommonDistributionTests.cs
index c2fce2c4..61779afb 100644
--- a/src/Numerics.Tests/DistributionTests/CommonDistributionTests.cs
+++ b/src/Numerics.Tests/DistributionTests/CommonDistributionTests.cs
@@ -79,6 +79,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
new InverseGamma(1.0, 1.0),
new InverseGaussian(1.0, 3.0),
new Laplace(1.0, 0.5),
+ new Logistic(0.0, 1.0),
new LogNormal(1.0, 1.0),
new Normal(0.0, 1.0),
new Pareto(1.0, 0.5),
diff --git a/src/Numerics.Tests/DistributionTests/Continuous/LogisticTests.cs b/src/Numerics.Tests/DistributionTests/Continuous/LogisticTests.cs
new file mode 100644
index 00000000..3b26ee00
--- /dev/null
+++ b/src/Numerics.Tests/DistributionTests/Continuous/LogisticTests.cs
@@ -0,0 +1,390 @@
+//
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+//
+// Copyright (c) 2009-2016 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.
+//
+
+using System;
+using System.Linq;
+using MathNet.Numerics.Distributions;
+using NUnit.Framework;
+
+namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
+{
+ using Random = System.Random;
+
+ ///
+ /// Logistic distribution tests.
+ ///
+ [TestFixture, Category("Distributions")]
+ public class LogisticTests
+ {
+ ///
+ /// Can create standard logistic.
+ ///
+ [Test]
+ public void CanCreateStandardLogistic()
+ {
+ var l = new Logistic();
+ Assert.AreEqual(0.0, l.Mean);
+ Assert.AreEqual(1.0, l.Scale);
+ }
+
+ ///
+ /// Can create logistic.
+ ///
+ /// Mean value.
+ /// Scale parameter value.
+ [TestCase(10.0, 0.1)]
+ [TestCase(-5.0, 1.0)]
+ [TestCase(0.0, 10.0)]
+ [TestCase(10.0, 100.0)]
+ [TestCase(-5.0, Double.PositiveInfinity)]
+ public void CanCreateLogistic(double mean, double scale)
+ {
+ var n = new Logistic(mean, scale);
+ Assert.AreEqual(mean, n.Mean);
+ Assert.AreEqual(scale, n.Scale);
+ }
+
+ ///
+ /// Logistic create fails with bad parameters.
+ ///
+ /// Mean value.
+ /// Scale parameter value.
+ [TestCase(Double.NaN, 1.0)]
+ [TestCase(1.0, Double.NaN)]
+ [TestCase(Double.NaN, Double.NaN)]
+ [TestCase(1.0, -1.0)]
+ public void LogisticCreateFailsWithBadParameters(double mean, double scale)
+ {
+ Assert.That(() => new Logistic(mean, scale), Throws.ArgumentException);
+ }
+
+ ///
+ /// Can create logistic from mean and scale parameter value.
+ ///
+ /// Mean value.
+ /// Scale parameter value.
+ [TestCase(10.0, 0.1)]
+ [TestCase(-5.0, 1.0)]
+ [TestCase(0.0, 10.0)]
+ [TestCase(10.0, 100.0)]
+ [TestCase(-5.0, Double.PositiveInfinity)]
+ public void CanCreateLogisticFromMeanAndScale(double mean, double scale)
+ {
+ var n = Logistic.WithMeanScale(mean, scale);
+ Assert.AreEqual(mean, n.Mean);
+ Assert.AreEqual(scale, n.Scale);
+ }
+
+ ///
+ /// Can create logistic from mean and standard deviation.
+ ///
+ /// Mean value.
+ /// Standard deviation value.
+ [TestCase(10.0, 0.1)]
+ [TestCase(-5.0, 1.0)]
+ [TestCase(0.0, 10.0)]
+ [TestCase(10.0, 100.0)]
+ [TestCase(-5.0, Double.PositiveInfinity)]
+ public void CanCreateLogisticFromMeanAndStdDev(double mean, double sdev)
+ {
+ var n = Logistic.WithMeanStdDev(mean, sdev);
+ Assert.AreEqual(mean, n.Mean);
+ Assert.AreEqual(sdev, n.StdDev);
+ }
+
+ ///
+ /// Can create logistic from mean and variance.
+ ///
+ /// Mean value.
+ /// Variance value.
+ [TestCase(10.0, 0.1)]
+ [TestCase(-5.0, 1.0)]
+ [TestCase(0.0, 10.0)]
+ [TestCase(10.0, 100.0)]
+ [TestCase(-5.0, Double.PositiveInfinity)]
+ public void CanCreateLogisticFromMeanAndVariance(double mean, double var)
+ {
+ var n = Logistic.WithMeanVariance(mean, var);
+ AssertHelpers.AlmostEqualRelative(mean, n.Mean, 15);
+ AssertHelpers.AlmostEqualRelative(var, n.Variance, 15);
+ }
+
+ ///
+ /// Can create logistic from mean and precision.
+ ///
+ /// Mean value.
+ /// Precision value.
+ [TestCase(10.0, 0.1)]
+ [TestCase(-5.0, 1.0)]
+ [TestCase(0.0, 10.0)]
+ [TestCase(10.0, 100.0)]
+ public void CanCreateLogisticFromMeanAndPrecision(double mean, double prec)
+ {
+ var n = Logistic.WithMeanPrecision(mean, prec);
+ AssertHelpers.AlmostEqualRelative(mean, n.Mean, 15);
+ AssertHelpers.AlmostEqualRelative(prec, n.Precision, 15);
+ }
+
+ ///
+ /// Validate ToString.
+ ///
+ [Test]
+ public void ValidateToString()
+ {
+ System.Threading.Thread.CurrentThread.CurrentCulture = System.Globalization.CultureInfo.InvariantCulture;
+ var n = new Logistic(1d, 2d);
+ Assert.AreEqual("Logistic(μ = 1, s = 2)", n.ToString());
+ }
+
+ ///
+ /// Validate entropy.
+ ///
+ /// Scale parameter value.
+ [TestCase(0.1)]
+ [TestCase(1.0)]
+ [TestCase(10.0)]
+ [TestCase(Double.PositiveInfinity)]
+ public void ValidateEntropy(double scale)
+ {
+ var n = new Logistic(1.0, scale);
+ Assert.AreEqual(Math.Log(scale) + 2, n.Entropy);
+ }
+
+ ///
+ /// Validate skewness.
+ ///
+ /// Scale parameter value.
+ [TestCase(0.1)]
+ [TestCase(1.0)]
+ [TestCase(10.0)]
+ [TestCase(Double.PositiveInfinity)]
+ public void ValidateSkewness(double scale)
+ {
+ var n = new Logistic(1.0, scale);
+ Assert.AreEqual(0.0, n.Skewness);
+ }
+
+ ///
+ /// Validate mean.
+ ///
+ /// Mean value.
+ [TestCase(Double.NegativeInfinity)]
+ [TestCase(-0.0)]
+ [TestCase(0.0)]
+ [TestCase(0.1)]
+ [TestCase(1.0)]
+ [TestCase(10.0)]
+ [TestCase(Double.PositiveInfinity)]
+ public void ValidateMode(double mean)
+ {
+ var n = new Logistic(mean, 1.0);
+ Assert.AreEqual(mean, n.Mode);
+ }
+
+ ///
+ /// Validate median.
+ ///
+ /// Mean value.
+ [TestCase(Double.NegativeInfinity)]
+ [TestCase(-0.0)]
+ [TestCase(0.0)]
+ [TestCase(0.1)]
+ [TestCase(1.0)]
+ [TestCase(10.0)]
+ [TestCase(Double.PositiveInfinity)]
+ public void ValidateMedian(double mean)
+ {
+ var n = new Logistic(mean, 1.0);
+ Assert.AreEqual(mean, n.Median);
+ }
+
+ ///
+ /// Validate minimum.
+ ///
+ [Test]
+ public void ValidateMinimum()
+ {
+ var n = new Logistic();
+ Assert.AreEqual(Double.NegativeInfinity, n.Minimum);
+ }
+
+ ///
+ /// Validate maximum.
+ ///
+ [Test]
+ public void ValidateMaximum()
+ {
+ var n = new Logistic();
+ Assert.AreEqual(Double.PositiveInfinity, n.Maximum);
+ }
+
+ ///
+ /// Can sample static.
+ ///
+ [Test]
+ public void CanSampleStatic()
+ {
+ Logistic.Sample(new Random(0), 0.0, 1.0);
+ }
+
+ ///
+ /// Can sample sequence static.
+ ///
+ [Test]
+ public void CanSampleSequenceStatic()
+ {
+ var ied = Logistic.Samples(new Random(0), 0.0, 1.0);
+ GC.KeepAlive(ied.Take(5).ToArray());
+ }
+
+ ///
+ /// Fail sample static with bad parameters.
+ ///
+ [Test]
+ public void FailSampleStatic()
+ {
+ Assert.That(() => { var d = Logistic.Sample(new Random(0), 0.0, -1.0); }, Throws.ArgumentException);
+ }
+
+ ///
+ /// Fail sample sequence static with bad parameters.
+ ///
+ [Test]
+ public void FailSampleSequenceStatic()
+ {
+ Assert.That(() => { var ied = Logistic.Samples(new Random(0), 0.0, -1.0).First(); }, Throws.ArgumentException);
+ }
+
+ ///
+ /// Can sample.
+ ///
+ [Test]
+ public void CanSample()
+ {
+ var n = new Logistic();
+ n.Sample();
+ }
+
+ ///
+ /// Can sample sequence.
+ ///
+ [Test]
+ public void CanSampleSequence()
+ {
+ var n = new Logistic();
+ var ied = n.Samples();
+ GC.KeepAlive(ied.Take(5).ToArray());
+ }
+
+ ///
+ /// Validate density.
+ ///
+ /// Input X value.
+ /// Expected value.
+ [TestCase(Double.NegativeInfinity, double.NaN)]
+ [TestCase(-5.0, 0.00332402833539508)]
+ [TestCase(-2.0, 0.01422651193986778)]
+ [TestCase(0.0, 0.03505185827255409)]
+ [TestCase(4.0, 0.11750185610079725)]
+ [TestCase(5.0, 0.12500000000000000)]
+ [TestCase(6.0, 0.11750185610079725)]
+ [TestCase(10.0, 0.03505185827255409)]
+ [TestCase(Double.PositiveInfinity, 0)]
+ public void ValidateDensity(double x, double d)
+ {
+ var n = Logistic.WithMeanScale(5.0, 2.0);
+ AssertHelpers.AlmostEqualRelative(d, n.Density(x), 9);
+ AssertHelpers.AlmostEqualRelative(d, Logistic.PDF(5.0, 2.0, x), 9);
+ }
+
+ ///
+ /// Validate density.
+ ///
+ /// Input X value.
+ /// Expected value.
+ [TestCase(Double.NegativeInfinity, double.NaN)]
+ [TestCase(-5.0, -5.70657787753818)]
+ [TestCase(-2.0, -4.25264801710519)]
+ [TestCase(0.0, -3.35092664914504)]
+ [TestCase(4.0, -2.14130114892016)]
+ [TestCase(5.0, -2.07944154167984)]
+ [TestCase(6.0, -2.14130114892016)]
+ [TestCase(10.0, -3.35092664914504)]
+ [TestCase(Double.PositiveInfinity, Double.NegativeInfinity)]
+ public void ValidateLogDensity(double x, double d)
+ {
+ var n = Logistic.WithMeanScale(5.0, 2.0);
+ AssertHelpers.AlmostEqualRelative(d, n.DensityLn(x), 9);
+ AssertHelpers.AlmostEqualRelative(d, Logistic.PDFLn(5.0, 2.0, x), 9);
+ }
+
+ ///
+ /// Validate cumulative distribution.
+ ///
+ /// Input X value.
+ /// Expected value.
+ [TestCase(Double.NegativeInfinity, 0.0)]
+ [TestCase(-5.0, 0.00669285092428486)]
+ [TestCase(-2.0, 0.0293122307513563)]
+ [TestCase(0.0, 0.0758581800212435)]
+ [TestCase(4.0, 0.377540668798145)]
+ [TestCase(5.0, 0.5)]
+ [TestCase(6.0, 0.622459331201855)]
+ [TestCase(10.0, 0.924141819978757)]
+ [TestCase(Double.PositiveInfinity, 1.0)]
+ public void ValidateCumulativeDistribution(double x, double p)
+ {
+ var n = Logistic.WithMeanScale(5.0, 2.0);
+ AssertHelpers.AlmostEqualRelative(p, n.CumulativeDistribution(x), 9);
+ AssertHelpers.AlmostEqualRelative(p, Logistic.CDF(5.0, 2.0, x), 9);
+ }
+
+ ///
+ /// Validate inverse cumulative distribution.
+ ///
+ /// Input X value.
+ /// Expected value.
+ [TestCase(Double.NegativeInfinity, 0.0)]
+ [TestCase(-5.0, 0.00669285092428486)]
+ [TestCase(-2.0, 0.0293122307513563)]
+ [TestCase(0.0, 0.0758581800212435)]
+ [TestCase(4.0, 0.377540668798145)]
+ [TestCase(5.0, 0.5)]
+ [TestCase(6.0, 0.622459331201855)]
+ [TestCase(10.0, 0.924141819978757)]
+ [TestCase(Double.PositiveInfinity, 1.0)]
+ public void ValidateInverseCumulativeDistribution(double x, double p)
+ {
+ var n = Logistic.WithMeanScale(5.0, 2.0);
+ AssertHelpers.AlmostEqualRelative(x, n.InverseCumulativeDistribution(p), 14);
+ AssertHelpers.AlmostEqualRelative(x, Logistic.InvCDF(5.0, 2.0, p), 14);
+ }
+
+ }
+}
diff --git a/src/Numerics/Distributions/Logistic.cs b/src/Numerics/Distributions/Logistic.cs
new file mode 100644
index 00000000..3c9c7ffd
--- /dev/null
+++ b/src/Numerics/Distributions/Logistic.cs
@@ -0,0 +1,514 @@
+//
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+//
+// Copyright (c) 2009-2015 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.
+//
+
+using System;
+using System.Collections.Generic;
+using MathNet.Numerics.Random;
+using MathNet.Numerics.Statistics;
+
+namespace MathNet.Numerics.Distributions
+{
+ ///
+ /// Continuous Univariate Logistic distribution.
+ /// For details about this distribution, see
+ /// Wikipedia - Logistic distribution.
+ ///
+ public class Logistic : IContinuousDistribution
+ {
+ System.Random _random;
+
+ readonly double _mean;
+ readonly double _scale;
+
+ ///
+ /// 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
+ /// random number generator.
+ ///
+ public Logistic()
+ : this(0.0, 1.0)
+ {
+ }
+
+ ///
+ /// 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
+ /// random number generator.
+ ///
+ /// The random number generator which is used to draw random samples.
+ public Logistic(System.Random randomSource)
+ : this(0.0, 1.0, randomSource)
+ {
+ }
+
+ ///
+ /// Initializes a new instance of the Logistic class with a particular mean and scale parameter. The
+ /// distribution will be initialized with the default random number generator.
+ ///
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ 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;
+ }
+
+ ///
+ /// Initializes a new instance of the Logistic class with a particular mean and standard deviation. The distribution will
+ /// be initialized with the default random number generator.
+ ///
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// The random number generator which is used to draw random samples.
+ 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;
+ }
+
+ ///
+ /// Constructs a logistic distribution from a mean and scale parameter.
+ ///
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// The random number generator which is used to draw random samples. Optional, can be null.
+ /// a logistic distribution.
+ public static Logistic WithMeanScale(double mean, double scale, System.Random randomSource = null)
+ {
+ return new Logistic(mean, scale, randomSource);
+ }
+
+ ///
+ /// Constructs a logistic distribution from a mean and standard deviation.
+ ///
+ /// The mean (μ) of the logistic distribution.
+ /// The standard deviation (σ) of the logistic distribution. Range: σ > 0.
+ /// The random number generator which is used to draw random samples. Optional, can be null.
+ /// a logistic distribution.
+ 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);
+ }
+
+ ///
+ /// Constructs a logistic distribution from a mean and variance.
+ ///
+ /// The mean (μ) of the logistic distribution.
+ /// The variance (σ^2) of the logistic distribution. Range: (σ^2) > 0.
+ /// The random number generator which is used to draw random samples. Optional, can be null.
+ /// A logistic distribution.
+ public static Logistic WithMeanVariance(double mean, double var, System.Random randomSource = null)
+ {
+ return WithMeanStdDev(mean, Math.Sqrt(var), randomSource);
+ }
+
+ ///
+ /// Constructs a logistic distribution from a mean and precision.
+ ///
+ /// The mean (μ) of the logistic distribution.
+ /// The precision of the logistic distribution. Range: precision > 0.
+ /// The random number generator which is used to draw random samples. Optional, can be null.
+ /// A logistic distribution.
+ public static Logistic WithMeanPrecision(double mean, double precision, System.Random randomSource = null)
+ {
+ return WithMeanVariance(mean, 1 / precision, randomSource);
+ }
+
+ ///
+ /// A string representation of the distribution.
+ ///
+ /// a string representation of the distribution.
+ public override string ToString()
+ {
+ return $"Logistic(μ = {_mean}, s = {_scale})";
+ }
+
+ ///
+ /// Tests whether the provided values are valid parameters for this distribution.
+ ///
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ public static bool IsValidParameterSet(double mean, double scale)
+ {
+ return scale > 0.0 && !double.IsNaN(mean);
+ }
+
+ ///
+ /// Gets the scale parameter of the Logistic distribution. Range: s > 0.
+ ///
+ public double Scale => _scale;
+
+ ///
+ /// Gets the mean (μ) of the logistic distribution.
+ ///
+ public double Mean => _mean;
+
+ ///
+ /// Gets the standard deviation (σ) of the logistic distribution. Range: σ > 0.
+ ///
+ public double StdDev => Math.Sqrt(Variance);
+
+ ///
+ /// Gets the variance of the logistic distribution.
+ ///
+ public double Variance => (Math.Pow(_scale, 2) * Math.Pow(Math.PI,2))/3;
+
+ ///
+ /// Gets the precision of the logistic distribution.
+ ///
+ public double Precision => 1.0/Variance;
+
+ ///
+ /// Gets the random number generator which is used to draw random samples.
+ ///
+ public System.Random RandomSource
+ {
+ get => _random;
+ set => _random = value ?? SystemRandomSource.Default;
+ }
+
+ ///
+ /// Gets the entropy of the logistic distribution.
+ ///
+ public double Entropy => Math.Log(_scale) + 2;
+
+ ///
+ /// Gets the skewness of the logistic distribution.
+ ///
+ public double Skewness => 0.0;
+
+ ///
+ /// Gets the mode of the logistic distribution.
+ ///
+ public double Mode => _mean;
+
+ ///
+ /// Gets the median of the logistic distribution.
+ ///
+ public double Median => _mean;
+
+ ///
+ /// Gets the minimum of the logistic distribution.
+ ///
+ public double Minimum => double.NegativeInfinity;
+
+ ///
+ /// Gets the maximum of the logistic distribution.
+ ///
+ public double Maximum => double.PositiveInfinity;
+
+ ///
+ /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
+ ///
+ /// The location at which to compute the density.
+ /// the density at .
+ ///
+ public double Density(double x)
+ {
+ return PDF(_mean, _scale, x);
+ }
+
+ ///
+ /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
+ ///
+ /// The location at which to compute the log density.
+ /// the log density at .
+ ///
+ public double DensityLn(double x)
+ {
+ return PDFLn(_mean, _scale, x);
+ }
+
+ ///
+ /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
+ ///
+ /// The location at which to compute the cumulative distribution function.
+ /// the cumulative distribution at location .
+ ///
+ public double CumulativeDistribution(double x)
+ {
+ return CDF(_mean, _scale, x);
+ }
+
+ ///
+ /// 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.
+ ///
+ /// The location at which to compute the inverse cumulative density.
+ /// the inverse cumulative density at .
+ ///
+ public double InverseCumulativeDistribution(double p)
+ {
+ return InvCDF(_mean, _scale, p);
+ }
+
+ ///
+ /// Generates a sample from the logistic distribution using the Box-Muller algorithm.
+ ///
+ /// a sample from the distribution.
+ public double Sample()
+ {
+ return SampleUnchecked(_random, _mean, _scale);
+ }
+
+ ///
+ /// Fills an array with samples generated from the distribution.
+ ///
+ public void Samples(double[] values)
+ {
+ SamplesUnchecked(_random, values, _mean, _scale);
+ }
+
+ ///
+ /// Generates a sequence of samples from the logistic distribution using the Box-Muller algorithm.
+ ///
+ /// a sequence of samples from the distribution.
+ public IEnumerable 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 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);
+ }
+ }
+
+ ///
+ /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
+ ///
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// The location at which to compute the density.
+ /// the density at .
+ ///
+ 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));
+ }
+
+ ///
+ /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
+ ///
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// The location at which to compute the density.
+ /// the log density at .
+ ///
+ 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)));
+ }
+
+ ///
+ /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
+ ///
+ /// The location at which to compute the cumulative distribution function.
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// the cumulative distribution at location .
+ ///
+ /// MATLAB: normcdf
+ 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));
+ }
+
+ ///
+ /// 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.
+ ///
+ /// The location at which to compute the inverse cumulative density.
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// the inverse cumulative density at .
+ ///
+ /// MATLAB: norminv
+ 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)));
+ }
+
+ ///
+ /// Generates a sample from the logistic distribution using the Box-Muller algorithm.
+ ///
+ /// The random number generator to use.
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// a sample from the distribution.
+ 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);
+ }
+
+ ///
+ /// Generates a sequence of samples from the logistic distribution using the Box-Muller algorithm.
+ ///
+ /// The random number generator to use.
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// a sequence of samples from the distribution.
+ public static IEnumerable 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);
+ }
+
+ ///
+ /// Fills an array with samples generated from the distribution.
+ ///
+ /// The random number generator to use.
+ /// The array to fill with the samples.
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// a sequence of samples from the distribution.
+ 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);
+ }
+
+ ///
+ /// Generates a sample from the logistic distribution using the Box-Muller algorithm.
+ ///
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// a sample from the distribution.
+ 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);
+ }
+
+ ///
+ /// Generates a sequence of samples from the logistic distribution using the Box-Muller algorithm.
+ ///
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// a sequence of samples from the distribution.
+ public static IEnumerable Samples(double mean, double scale)
+ {
+ if (scale <= 0.0)
+ {
+ throw new ArgumentException("Invalid parametrization for the distribution.");
+ }
+
+ return SamplesUnchecked(SystemRandomSource.Default, mean, scale);
+ }
+
+ ///
+ /// Fills an array with samples generated from the distribution.
+ ///
+ /// The array to fill with the samples.
+ /// The mean (μ) of the logistic distribution.
+ /// The scale (s) of the logistic distribution. Range: s > 0.
+ /// a sequence of samples from the distribution.
+ 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);
+ }
+ }
+}