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Distributions: adapt Pareto, add InvCDF

optimization-1
Christoph Ruegg 13 years ago
parent
c710944044
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b8c68e9775
2 changed files with 111 additions and 67 deletions
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  1. 113
      src/Numerics/Distributions/Pareto.cs
  2. 65
      src/UnitTests/DistributionTests/Continuous/ParetoTests.cs

113
src/Numerics/Distributions/Pareto.cs
View File

@ -87,17 +87,6 @@ namespace MathNet.Numerics.Distributions
return "Pareto(xm = " + _scale + ", α = " + _shape + ")";
}
/// <summary>
/// Checks whether the parameters of the distribution are valid.
/// </summary>
/// <param name="scale">The scale (xm) of the distribution. Range: xm > 0.</param>
/// <param name="shape">The shape (α) of the distribution. Range: α > 0.</param>
/// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
static bool IsValidParameterSet(double scale, double shape)
{
return scale > 0.0 && shape > 0.0;
}
/// <summary>
/// Sets the parameters of the distribution after checking their validity.
/// </summary>
@ -106,7 +95,7 @@ namespace MathNet.Numerics.Distributions
/// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
void SetParameters(double scale, double shape)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(scale, shape))
if (scale <= 0.0 || shape <= 0.0 || Double.IsNaN(scale) || Double.IsNaN(shape))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
@ -235,6 +224,7 @@ 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)
{
return _shape*Math.Pow(_scale, _shape)/Math.Pow(x, _shape + 1.0);
@ -245,9 +235,10 @@ 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(Density(x));
return Math.Log(_shape) + _shape*Math.Log(_scale) - (_shape + 1.0)*Math.Log(x);
}
/// <summary>
@ -255,21 +246,22 @@ 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)
{
return 1.0 - Math.Pow(_scale/x, _shape);
}
/// <summary>
/// Generates a sample from the Pareto distribution without doing parameter checking.
/// 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="rnd">The random number generator to use.</param>
/// <param name="scale">The scale (xm) of the distribution. Range: xm > 0.</param>
/// <param name="shape">The shape (α) of the distribution. Range: α > 0.</param>
/// <returns>a random number from the Pareto distribution.</returns>
static double SampleUnchecked(System.Random rnd, double scale, double shape)
/// <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 scale*Math.Pow(rnd.NextDouble(), -1.0/shape);
return _scale*Math.Pow(1.0 - p, -1.0/_shape);
}
/// <summary>
@ -278,7 +270,7 @@ namespace MathNet.Numerics.Distributions
/// <returns>A random number from this distribution.</returns>
public double Sample()
{
return SampleUnchecked(_random, _scale, _shape);
return _scale*Math.Pow(_random.NextDouble(), -1.0/_shape);
}
/// <summary>
@ -287,12 +279,74 @@ namespace MathNet.Numerics.Distributions
/// <returns>a sequence of samples from the distribution.</returns>
public IEnumerable<double> Samples()
{
var power = -1.0/_shape;
while (true)
{
yield return SampleUnchecked(_random, _scale, _shape);
yield return _scale*Math.Pow(_random.NextDouble(), power);
}
}
/// <summary>
/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
/// </summary>
/// <param name="scale">The scale (xm) of the distribution. Range: xm > 0.</param>
/// <param name="shape">The shape (α) of the distribution. Range: α > 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 scale, double shape, double x)
{
if (scale <= 0.0 || shape <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
return shape*Math.Pow(scale, shape)/Math.Pow(x, shape + 1.0);
}
/// <summary>
/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
/// </summary>
/// <param name="scale">The scale (xm) of the distribution. Range: xm > 0.</param>
/// <param name="shape">The shape (α) of the distribution. Range: α > 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 scale, double shape, double x)
{
if (scale <= 0.0 || shape <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
return Math.Log(shape) + shape*Math.Log(scale) - (shape + 1.0)*Math.Log(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="scale">The scale (xm) of the distribution. Range: xm > 0.</param>
/// <param name="shape">The shape (α) of the distribution. Range: α > 0.</param>
/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
/// <seealso cref="CumulativeDistribution"/>
public static double CDF(double scale, double shape, double x)
{
if (scale <= 0.0 || shape <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
return 1.0 - Math.Pow(scale/x, shape);
}
/// <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="scale">The scale (xm) of the distribution. Range: xm > 0.</param>
/// <param name="shape">The shape (α) of the distribution. Range: α > 0.</param>
/// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
/// <seealso cref="InverseCumulativeDistribution"/>
public static double InvCDF(double scale, double shape, double p)
{
if (scale <= 0.0 || shape <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
return scale*Math.Pow(1.0 - p, -1.0/shape);
}
/// <summary>
/// Generates a sample from the distribution.
/// </summary>
@ -302,12 +356,9 @@ namespace MathNet.Numerics.Distributions
/// <returns>a sample from the distribution.</returns>
public static double Sample(System.Random rnd, double scale, double shape)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(scale, shape))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
if (scale <= 0.0 || shape <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
return SampleUnchecked(rnd, scale, shape);
return scale*Math.Pow(rnd.NextDouble(), -1.0/shape);
}
/// <summary>
@ -319,14 +370,12 @@ namespace MathNet.Numerics.Distributions
/// <returns>a sequence of samples from the distribution.</returns>
public static IEnumerable<double> Samples(System.Random rnd, double scale, double shape)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(scale, shape))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
if (scale <= 0.0 || shape <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
var power = -1.0 / shape;
while (true)
{
yield return SampleUnchecked(rnd, scale, shape);
yield return scale*Math.Pow(rnd.NextDouble(), power);
}
}
}

65
src/UnitTests/DistributionTests/Continuous/ParetoTests.cs
View File

@ -282,40 +282,53 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
Assert.AreEqual(Double.PositiveInfinity, n.Maximum);
}
/// <summary>
/// Validate density.
/// </summary>
/// <param name="scale">Scale value.</param>
/// <param name="shape">Shape value.</param>
/// <param name="x">Input X value.</param>
[TestCase(1, 1, 1, 1)]
[TestCase(1, 1, 1.5, 4/9.0)]
[TestCase(1, 1, 5, 1/25.0)]
[TestCase(1, 1, 50, 1/2500.0)]
[TestCase(1, 4, 1, 4)]
[TestCase(1, 4, 1.5, 128/243.0)]
[TestCase(1, 4, 50, 1/78125000.0)]
[TestCase(3, 2, 3, 2/3.0)]
[TestCase(3, 2, 5, 18/125.0)]
[TestCase(25, 100, 50, 1.5777218104420236e-30)]
[TestCase(100, 25, 150, 6.6003546737276816e-6)]
public void ValidateDensity(double scale, double shape, double x, double expected)
{
var dist = new Pareto(scale, shape);
Assert.AreEqual(expected, dist.Density(x), 1e-12);
Assert.AreEqual(expected, Pareto.PDF(scale, shape, x), 1e-12);
Assert.AreEqual(Math.Log(expected), dist.DensityLn(x), 1e-12);
Assert.AreEqual(Math.Log(expected), Pareto.PDFLn(scale, shape, x), 1e-12);
}
[TestCase(0.1, 0.1, 0.1)]
[TestCase(1.0, 1.0, 1.0)]
[TestCase(5.0, 5.0, 2.0)]
[TestCase(7.0, 7.0, 10.0)]
[TestCase(10.0, 10.0, 12.0)]
[TestCase(Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)]
public void ValidateDensity(double scale, double shape, double x)
public void ValidateCumulativeDistribution(double scale, double shape, double x)
{
var n = new Pareto(scale, shape);
Assert.AreEqual(shape * Math.Pow(scale, shape) / Math.Pow(x, shape + 1.0), n.Density(x));
double expected = 1.0 - Math.Pow(scale/x, shape);
Assert.AreEqual(expected, n.CumulativeDistribution(x));
Assert.AreEqual(expected, Pareto.CDF(scale, shape, x));
}
/// <summary>
/// Validate density log.
/// </summary>
/// <param name="scale">Scale value.</param>
/// <param name="shape">Shape value.</param>
/// <param name="x">Input X value.</param>
[TestCase(0.1, 0.1, 0.1)]
[TestCase(1.0, 1.0, 1.0)]
[TestCase(5.0, 5.0, 2.0)]
[TestCase(7.0, 7.0, 10.0)]
[TestCase(10.0, 10.0, 12.0)]
[TestCase(Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)]
public void ValidateDensityLn(double scale, double shape, double x)
public void ValidateInverseCumulativeDistribution(double scale, double shape, double x)
{
var n = new Pareto(scale, shape);
Assert.AreEqual(Math.Log(n.Density(x)), n.DensityLn(x));
double cdf = 1.0 - Math.Pow(scale / x, shape);
Assert.AreEqual(x, n.InverseCumulativeDistribution(cdf), 1e-12);
Assert.AreEqual(x, Pareto.InvCDF(scale, shape, cdf), 1e-12);
}
/// <summary>
@ -338,23 +351,5 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
var ied = n.Samples();
ied.Take(5).ToArray();
}
/// <summary>
/// Validate cumulative distribution.
/// </summary>
/// <param name="scale">Scale value.</param>
/// <param name="shape">Shape value.</param>
/// <param name="x">Input X value.</param>
[TestCase(0.1, 0.1, 0.1)]
[TestCase(1.0, 1.0, 1.0)]
[TestCase(5.0, 5.0, 2.0)]
[TestCase(7.0, 7.0, 10.0)]
[TestCase(10.0, 10.0, 12.0)]
[TestCase(Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)]
public void ValidateCumulativeDistribution(double scale, double shape, double x)
{
var n = new Pareto(scale, shape);
Assert.AreEqual(1.0 - Math.Pow(scale / x, shape), n.CumulativeDistribution(x));
}
}
}

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