public void TestStarUniformDistribution()
{
IContinuousDistribution distribution = new Gamma(9, 1/5000.0);
Console.WriteLine(distribution.CumulativeDistribution(30000));
//IContinuousDistribution distribution = new Gamma(3, 0.05);
for (double d = 0; d < 50000; d = d + 1000)
{
//Console.WriteLine(Gamma.PDF(3, 0.05, d));
//Console.WriteLine(Gamma.CDF(3, 0.05, d));
Console.WriteLine("" + d + ": " + distribution.CumulativeDistribution(d));
}
}
public void SetupDistributions()
{
dists = new IDistribution[8];
dists[0] = new Beta(1.0, 1.0);
dists[1] = new ContinuousUniform(0.0, 1.0);
dists[2] = new Gamma(1.0, 1.0);
dists[3] = new Normal(0.0, 1.0);
dists[4] = new Bernoulli(0.6);
dists[5] = new Weibull(1.0, 1.0);
dists[6] = new DiscreteUniform(1, 10);
dists[7] = new LogNormal(1.0, 1.0);
}
public void ValidateInverseCumulativeDistribution(int shape, double invScale, double x, double cdf)
{
var gamma = new Gamma(shape, invScale);
Assert.That(gamma.InverseCumulativeDistribution(cdf), Is.EqualTo(x).Within(10));
Assert.That(Gamma.InvCDF(shape, invScale, cdf), Is.EqualTo(x).Within(10));
}
public void SetShapeFailsWithNegativeShape()
{
var n = new Gamma(1.0, 1.0);
Assert.That(() => n.Shape = -1.0, Throws.ArgumentException);
}
public void ValidateDensityLn(int shape, double invScale, double x, double pdfln)
{
var n = new Gamma(shape, invScale);
AssertHelpers.AlmostEqualRelative(pdfln, n.DensityLn(x), 13);
AssertHelpers.AlmostEqualRelative(pdfln, Gamma.PDFLn(shape, invScale, x), 13);
}
public void SetInvScaleFailsWithNegativeInvScale()
{
var n = new Gamma(1.0, 1.0);
Assert.Throws<ArgumentOutOfRangeException>(() => n.Rate = -1.0);
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Gamma_distribution">Gamma distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Gamma distribution class with parameter Shape = 1, Scale = 0.5.
var gamma = new Gamma(1, 2.0);
Console.WriteLine(@"1. Initialize the new instance of the Gamma distribution class with parameters Shape = {0}, Scale = {1}", gamma.Shape, gamma.Scale);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", gamma);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", gamma.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", gamma.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", gamma.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", gamma.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", gamma.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", gamma.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", gamma.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", gamma.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", gamma.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", gamma.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", gamma.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the Gamma distribution
Console.WriteLine(@"3. Generate 10 samples of the Gamma distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(gamma.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Gamma(1, 2) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Gamma(1, 2) distribution and display histogram");
var data = new double[100000];
Gamma.Samples(data, 1, 2);
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Gamma(8) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Gamma(5, 1) distribution and display histogram");
Gamma.Samples(data, 5, 1);
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateSkewness(double shape, double invScale, double skewness)
{
var n = new Gamma(shape, invScale);
AssertHelpers.AlmostEqualRelative(skewness, n.Skewness, 15);
}
/// <summary>
/// Generates a sequence of samples from the distribution.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="shape">The shape (k) of the Erlang distribution. Range: k ≥ 0.</param>
/// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.</param>
/// <returns>a sequence of samples from the distribution.</returns>
public static IEnumerable <double> Samples(System.Random rnd, int shape, double rate)
{
return(Gamma.Samples(rnd, shape, rate));
}
static double SampleUnchecked(System.Random rnd, double shape, double scale)
{
return(1.0 / Gamma.SampleUnchecked(rnd, shape, scale));
}
static IEnumerable <double> SamplesUnchecked(System.Random rnd, double shape, double scale)
{
return(Gamma.SamplesUnchecked(rnd, shape, scale).Select(z => 1.0 / z));
}
/// <summary>
/// Fills an array with samples generated from the distribution.
/// </summary>
/// <param name="values">The array to fill with the samples.</param>
/// <param name="shape">The shape (k) of the Erlang distribution. Range: k ≥ 0.</param>
/// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.</param>
/// <returns>a sequence of samples from the distribution.</returns>
public static void Samples(double[] values, int shape, double rate)
{
Gamma.Samples(values, shape, rate);
}
/// <summary>
/// Generates a sequence of samples from the NormalGamma distribution
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="meanLocation">The location of the mean.</param>
/// <param name="meanScale">The scale of the mean.</param>
/// <param name="precisionShape">The shape of the precision.</param>
/// <param name="precisionInvScale">The inverse scale of the precision.</param>
/// <returns>a sequence of samples from the distribution.</returns>
public static IEnumerable <MeanPrecisionPair> Samples(System.Random rnd, double meanLocation, double meanScale, double precisionShape, double precisionInvScale)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(meanLocation, meanScale, precisionShape, precisionInvScale))
{
throw new ArgumentException(Resources.InvalidDistributionParameters);
}
while (true)
{
var mp = new MeanPrecisionPair();
// Sample the precision.
mp.Precision = double.IsPositiveInfinity(precisionInvScale) ? precisionShape : Gamma.Sample(rnd, precisionShape, precisionInvScale);
// Sample the mean.
mp.Mean = meanScale == 0.0 ? meanLocation : Normal.Sample(rnd, meanLocation, Math.Sqrt(1.0 / (meanScale * mp.Precision)));
yield return(mp);
}
}
/// <summary>
/// Generates a sequence of samples from the distribution.
/// </summary>
/// <param name="shape">The shape (k) of the Erlang distribution. Range: k ≥ 0.</param>
/// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.</param>
/// <returns>a sequence of samples from the distribution.</returns>
public static IEnumerable <double> Samples(int shape, double rate)
{
return(Gamma.Samples(shape, rate));
}
/// <summary>
/// Generates a sample from the distribution.
/// </summary>
/// <param name="shape">The shape (k) of the Erlang distribution. Range: k ≥ 0.</param>
/// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.</param>
/// <returns>a sample from the distribution.</returns>
public static double Sample(int shape, double rate)
{
return(Gamma.Sample(shape, rate));
}
/// <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="shape">The shape (k) of the Erlang distribution. Range: k ≥ 0.</param>
/// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.</param>
/// <returns>a sequence of samples from the distribution.</returns>
public static void Samples(System.Random rnd, double[] values, int shape, double rate)
{
Gamma.Samples(rnd, values, shape, rate);
}
public void ValidateMean(double shape, double invScale, double mean)
{
var n = new Gamma(shape, invScale);
Assert.AreEqual(mean, n.Mean);
}
/// <summary>
/// Samples student-t distributed random variables.
/// </summary>
/// <remarks>The algorithm is method 2 in section 5, chapter 9
/// in L. Devroye's "Non-Uniform Random Variate Generation"</remarks>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="location">The location (μ) of the distribution.</param>
/// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
/// <param name="freedom">The degrees of freedom (ν) for the distribution. Range: ν > 0.</param>
/// <returns>a random number from the standard student-t distribution.</returns>
static double SampleUnchecked(System.Random rnd, double location, double scale, double freedom)
{
var gamma = Gamma.SampleUnchecked(rnd, 0.5 * freedom, 0.5);
return(Normal.Sample(rnd, location, scale * Math.Sqrt(freedom / gamma)));
}
public void ValidateMinimum()
{
var n = new Gamma(1.0, 1.0);
Assert.AreEqual(0.0, n.Minimum);
}
/// <summary>
/// Draws a random sample from the distribution.
/// </summary>
/// <returns>A random number from this distribution.</returns>
public double Sample()
{
return(1.0 / Gamma.Sample(_random, _shape, _scale));
}
public void ValidateToString()
{
var n = new Gamma(1d, 2d);
Assert.AreEqual("Gamma(α = 1, β = 2)", n.ToString());
}
/// <summary>
/// Generates a sequence of samples from the Cauchy distribution.
/// </summary>
/// <returns>a sequence of samples from the distribution.</returns>
public IEnumerable <double> Samples()
{
return(Gamma.Samples(_random, _shape, _scale).Select(z => 1.0 / z));
}
public void ValidateDensity(int shape, double invScale, double x, double pdf)
{
var n = new Gamma(shape, invScale);
AssertHelpers.AlmostEqual(pdf, n.Density(x), 14);
AssertHelpers.AlmostEqual(pdf, Gamma.PDF(shape, invScale, x), 14);
}
public void SetScaleFailsWithNegativeScale()
{
var n = new Gamma(1.0, 1.0);
n.Scale = -1.0;
}
public void SetShapeFailsWithNegativeShape()
{
var n = new Gamma(1.0, 1.0);
Assert.Throws<ArgumentOutOfRangeException>(() => n.Shape = -1.0);
}
public void SetShapeFailsWithNegativeShape()
{
var n = new Gamma(1.0, 1.0);
n.Shape = -1.0;
}
public void SetInvScaleFailsWithNegativeInvScale()
{
var n = new Gamma(1.0, 1.0);
Assert.That(() => n.Rate = -1.0, Throws.ArgumentException);
}
public void ValidateDensityLn(double shape, double invScale, double x, double pdfln)
{
var n = new Gamma(shape, invScale);
AssertHelpers.AlmostEqual(pdfln, n.DensityLn(x), 14);
}
public void ValidateCumulativeDistribution(int shape, double invScale, double x, double cdf)
{
var gamma = new Gamma(shape, invScale);
Assert.That(gamma.CumulativeDistribution(x), Is.EqualTo(cdf).Within(13));
Assert.That(Gamma.CDF(shape, invScale, x), Is.EqualTo(cdf).Within(13));
}
public void ValidateMaximum()
{
var n = new Gamma(1.0, 1.0);
AssertEx.AreEqual<double>(System.Double.PositiveInfinity, n.Maximum);
}
public void ValidateEntropy(double shape, double invScale, double entropy)
{
var n = new Gamma(shape, invScale);
AssertHelpers.AlmostEqualRelative(entropy, n.Entropy, 12);
}
public void ValidateMedian(double shape, double invScale)
{
var n = new Gamma(shape, invScale);
var median = n.Median;
}
public void ValidateMaximum()
{
var n = new Gamma(1.0, 1.0);
Assert.AreEqual(Double.PositiveInfinity, n.Maximum);
}
public void ValidateToString()
{
var n = new Gamma(1.0, 2.0);
AssertEx.AreEqual<string>("Gamma(Shape = 1, Inverse Scale = 2)", n.ToString());
}
public void ValidateMedian()
{
var n = new Gamma(0.0, 0.0);
Assert.Throws<NotSupportedException>(() => { var median = n.Median; });
}
public void CanCreateGamma(double shape, double invScale)
{
var n = new Gamma(shape, invScale);
AssertEx.AreEqual<double>(shape, n.Shape);
AssertEx.AreEqual<double>(invScale, n.InvScale);
}
public void ValidateMode(double shape, double invScale, double mode)
{
var n = new Gamma(shape, invScale);
Assert.AreEqual(mode, n.Mode);
}
public void CanCreateGamma(double shape, double invScale)
{
var n = new Gamma(shape, invScale);
Assert.AreEqual(shape, n.Shape);
Assert.AreEqual(invScale, n.Rate);
}
public void ValidateStdDev(double shape, double invScale, double sdev)
{
var n = new Gamma(shape, invScale);
AssertHelpers.AlmostEqualRelative(sdev, n.StdDev, 15);
}
/// <summary>
/// Fills an array with samples generated from the distribution.
/// </summary>
public void Samples(double[] values)
{
Gamma.SamplesUnchecked(_random, values, _shape, _rate);
}
public void ValidateVariance(double shape, double invScale, double var)
{
var n = new Gamma(shape, invScale);
AssertHelpers.AlmostEqualRelative(var, n.Variance, 15);
}
/// <summary>
/// Generates a sample from the distribution.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="shape">The shape (k) of the Erlang distribution. Range: k ≥ 0.</param>
/// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.</param>
/// <returns>a sample from the distribution.</returns>
public static double Sample(System.Random rnd, int shape, double rate)
{
return(Gamma.Sample(rnd, shape, rate));
}
public void ValidateCumulativeDistribution(int shape, double invScale, double x, double cdf)
{
var n = new Gamma(shape, invScale);
AssertHelpers.AlmostEqual(cdf, n.CumulativeDistribution(x), 14);
AssertHelpers.AlmostEqual(cdf, Gamma.CDF(shape, invScale, x), 14);
}
/// <summary>
/// Generates a sample from the Erlang distribution.
/// </summary>
/// <returns>a sample from the distribution.</returns>
public double Sample()
{
return(Gamma.SampleUnchecked(_random, _shape, _rate));
}
