tsai
/
mathnet-numerics
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity
Browse Source

Distributions: adapt Exponential, add InvCDF

pull/163/head
Christoph Ruegg 13 years ago
parent
d2c907f8e3
commit
cef08e67d1
2 changed files with 115 additions and 44 deletions
Whitespace
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Split View
Diff Options
Show Stats Download Patch File Download Diff File
  1. 128
      src/Numerics/Distributions/Exponential.cs
  2. 31
      src/UnitTests/DistributionTests/Continuous/ExponentialTests.cs

128
src/Numerics/Distributions/Exponential.cs
View File

@ -80,16 +80,6 @@ namespace MathNet.Numerics.Distributions
return "Exponential(λ = " + _rate + ")";
}
/// <summary>
/// Checks whether the parameters of the distribution are valid.
/// </summary>
/// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
/// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
static bool IsValidParameterSet(double rate)
{
return rate >= 0.0;
}
/// <summary>
/// Sets the parameters of the distribution after checking their validity.
/// </summary>
@ -97,7 +87,7 @@ namespace MathNet.Numerics.Distributions
/// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
void SetParameters(double rate)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(rate))
if (rate < 0.0 || Double.IsNaN(rate))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
@ -200,14 +190,10 @@ namespace MathNet.Numerics.Distributions
/// </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)
{
if (x >= 0.0)
{
return _rate*Math.Exp(-_rate*x);
}
return 0.0;
return x < 0.0 ? 0.0 : _rate*Math.Exp(-_rate*x);
}
/// <summary>
@ -215,6 +201,7 @@ namespace MathNet.Numerics.Distributions
/// </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 Math.Log(_rate) - (_rate*x);
@ -225,14 +212,43 @@ namespace MathNet.Numerics.Distributions
/// </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)
{
if (x >= 0.0)
return x < 0.0 ? 0.0 : 1.0 - Math.Exp(-_rate*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 p >= 1.0 ? double.PositiveInfinity : -Math.Log(1 - p)/_rate;
}
/// <summary>
/// Draws a random sample from the distribution.
/// </summary>
/// <returns>A random number from this distribution.</returns>
public double Sample()
{
return SampleUnchecked(_random, _rate);
}
/// <summary>
/// Generates a sequence of samples from the Exponential distribution.
/// </summary>
/// <returns>a sequence of samples from the distribution.</returns>
public IEnumerable<double> Samples()
{
while (true)
{
return 1.0 - Math.Exp(-_rate*x);
yield return SampleUnchecked(_random, _rate);
}
return 0.0;
}
/// <summary>
@ -249,28 +265,64 @@ namespace MathNet.Numerics.Distributions
r = rnd.NextDouble();
}
return -Math.Log(r)/rate;
return -Math.Log(r) / rate;
}
/// <summary>
/// Draws a random sample from the distribution.
/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
/// </summary>
/// <returns>A random number from this distribution.</returns>
public double Sample()
/// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 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 rate, double x)
{
return SampleUnchecked(_random, _rate);
if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
return x < 0.0 ? 0.0 : rate*Math.Exp(-rate*x);
}
/// <summary>
/// Generates a sequence of samples from the Exponential distribution.
/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
/// </summary>
/// <returns>a sequence of samples from the distribution.</returns>
public IEnumerable<double> Samples()
/// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 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 rate, double x)
{
while (true)
{
yield return SampleUnchecked(_random, _rate);
}
if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
return Math.Log(rate) - (rate*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="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
/// <seealso cref="CumulativeDistribution"/>
public static double CDF(double rate, double x)
{
if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
return x < 0.0 ? 0.0 : 1.0 - Math.Exp(-rate*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>
/// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
/// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
/// <seealso cref="InverseCumulativeDistribution"/>
public static double InvCDF(double rate, double p)
{
if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
return p >= 1.0 ? double.PositiveInfinity : -Math.Log(1 - p)/rate;
}
/// <summary>
@ -281,10 +333,7 @@ namespace MathNet.Numerics.Distributions
/// <returns>A random number from this distribution.</returns>
public static double Sample(System.Random rnd, double rate)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(rate))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
return SampleUnchecked(rnd, rate);
}
@ -297,10 +346,7 @@ namespace MathNet.Numerics.Distributions
/// <returns>a sequence of samples from the distribution.</returns>
public static IEnumerable<double> Samples(System.Random rnd, double rate)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(rate))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
while (true)
{

31
src/UnitTests/DistributionTests/Continuous/ExponentialTests.cs
View File

@ -266,11 +266,13 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
var n = new Exponential(lambda);
if (x >= 0)
{
Assert.AreEqual(lambda * Math.Exp(-lambda * x), n.Density(x));
Assert.AreEqual(lambda*Math.Exp(-lambda*x), n.Density(x));
Assert.AreEqual(lambda*Math.Exp(-lambda*x), Exponential.PDF(lambda, x));
}
else
{
Assert.AreEqual(0.0, n.Density(lambda));
Assert.AreEqual(0.0, Exponential.PDF(lambda, lambda));
}
}
@ -302,7 +304,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
public void ValidateDensityLn(double lambda, double x)
{
var n = new Exponential(lambda);
Assert.AreEqual(Math.Log(lambda) - (lambda * x), n.DensityLn(x));
Assert.AreEqual(Math.Log(lambda) - (lambda*x), n.DensityLn(x));
Assert.AreEqual(Math.Log(lambda) - (lambda*x), Exponential.PDFLn(lambda, x));
}
/// <summary>
@ -356,12 +359,34 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
var n = new Exponential(lambda);
if (x >= 0.0)
{
Assert.AreEqual(1.0 - Math.Exp(-lambda * x), n.CumulativeDistribution(x));
Assert.AreEqual(1.0 - Math.Exp(-lambda*x), n.CumulativeDistribution(x));
Assert.AreEqual(1.0 - Math.Exp(-lambda*x), Exponential.CDF(lambda, x));
}
else
{
Assert.AreEqual(0.0, n.CumulativeDistribution(x));
Assert.AreEqual(0.0, Exponential.CDF(lambda, x));
}
}
/// <summary>
/// Validate inverse cumulative distribution.
/// </summary>
/// <param name="lambda">Lambda value.</param>
/// <param name="x">Input X value.</param>
[TestCase(0.1, 0.0)]
[TestCase(1.0, 0.0)]
[TestCase(10.0, 0.0)]
[TestCase(10.0, 0.1)]
[TestCase(1.0, 1.0)]
[TestCase(0.1, Double.PositiveInfinity)]
[TestCase(1.0, Double.PositiveInfinity)]
[TestCase(10.0, Double.PositiveInfinity)]
public void ValidateInverseCumulativeDistribution(double lambda, double x)
{
var n = new Exponential(lambda);
Assert.AreEqual(x, n.InverseCumulativeDistribution(1.0 - Math.Exp(-lambda*x)));
Assert.AreEqual(x, Exponential.InvCDF(lambda, 1.0 - Math.Exp(-lambda*x)));
}
}
}

Write Preview
Loading…
Cancel
Save