public void CanCreateInverseGamma([Values(0.1, 1.0, Double.PositiveInfinity)] double a, [Values(0.1, 1.0, Double.PositiveInfinity)] double b)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(a, n.Shape);
Assert.AreEqual(b, n.Scale);
}
public void ValidateToString()
{
System.Threading.Thread.CurrentThread.CurrentCulture = CultureInfo.InvariantCulture;
var n = new InverseGamma(1.1d, 2.1d);
Assert.AreEqual("InverseGamma(α = 1.1, β = 2.1)", n.ToString());
}
public void CanSampleSequence()
{
var n = new InverseGamma(1.0, 1.0);
var ied = n.Samples();
GC.KeepAlive(ied.Take(5).ToArray());
}
public void CanCreateInverseGamma(double a, double b)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(a, n.Shape);
Assert.AreEqual(b, n.Scale);
}
public void ValidateDensityLn(double a, double b, double x)
{
var n = new InverseGamma(a, b);
double expected = Math.Log(Math.Pow(b, a) * Math.Pow(x, -a - 1.0) * Math.Exp(-b / x) / SpecialFunctions.Gamma(a));
Assert.AreEqual(expected, n.DensityLn(x));
Assert.AreEqual(expected, InverseGamma.PDFLn(a, b, x));
}
public void ValidateCumulativeDistribution(double a, double b, double x)
{
var n = new InverseGamma(a, b);
double expected = SpecialFunctions.GammaUpperRegularized(a, b / x);
Assert.AreEqual(expected, n.CumulativeDistribution(x));
Assert.AreEqual(expected, InverseGamma.CDF(a, b, x));
}
public void ValidateDensityLn(
[Values(0.1, 0.1, 0.1, 1.0, 1.0, 1.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double a,
[Values(0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity)] double b,
[Values(1.2, 2.0, 1.1, 1.5, 1.2, 1.5, 5.0, 2.5, 1.0)] double x)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(Math.Log(n.Density(x)), n.DensityLn(x));
}
public void ValidateStdDev([Values(0.1, 1.0, Double.PositiveInfinity)] double a, [Values(0.1, 1.0, Double.PositiveInfinity)] double b)
{
var n = new InverseGamma(a, b);
if (a > 2)
{
Assert.AreEqual(b / ((a - 1.0) * Math.Sqrt(a - 2.0)), n.StdDev);
}
}
public void ValidateVariance([Values(0.1, 1.0, Double.PositiveInfinity)] double a, [Values(0.1, 1.0, Double.PositiveInfinity)] double b)
{
var n = new InverseGamma(a, b);
if (a > 2)
{
Assert.AreEqual(b * b / ((a - 1.0) * (a - 1.0) * (a - 2.0)), n.Variance);
}
}
public void ValidateMean([Values(0.1, 1.0, Double.PositiveInfinity)] double a, [Values(0.1, 1.0, Double.PositiveInfinity)] double b)
{
var n = new InverseGamma(a, b);
if (a > 1)
{
Assert.AreEqual(b / (a - 1.0), n.Mean);
}
}
public void ValidateCumulativeDistribution(
[Values(0.1, 0.1, 0.1, 1.0, 1.0, 1.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double a,
[Values(0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity)] double b,
[Values(1.2, 2.0, 1.1, 1.5, 1.2, 1.5, 5.0, 2.5, 1.0)] double x)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(SpecialFunctions.GammaUpperRegularized(a, b / x), n.CumulativeDistribution(x));
}
public void ValidateMean(double a, double b)
{
var n = new InverseGamma(a, b);
if (a > 1)
{
Assert.AreEqual(b / (a - 1.0), n.Mean);
}
}
public void ValidateStdDev(double a, double b)
{
var n = new InverseGamma(a, b);
if (a > 2)
{
Assert.AreEqual(b / ((a - 1.0) * Math.Sqrt(a - 2.0)), n.StdDev);
}
}
public void ValidateVariance(double a, double b)
{
var n = new InverseGamma(a, b);
if (a > 2)
{
Assert.AreEqual(b * b / ((a - 1.0) * (a - 1.0) * (a - 2.0)), n.Variance);
}
}
public void ValidateDensity(double a, double b, double x)
{
var n = new InverseGamma(a, b);
if (x >= 0)
{
Assert.AreEqual <double>(Math.Pow(b, a) * Math.Pow(x, -a - 1.0) * Math.Exp(-b / x) / SpecialFunctions.Gamma(a), n.Density(x));
}
else
{
Assert.AreEqual <double>(0.0, n.Density(x));
}
}
public void ValidateDensity(
[Values(0.1, 0.1, 0.1, 1.0, 1.0, 1.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double a,
[Values(0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity)] double b,
[Values(1.2, 2.0, 1.1, 1.5, 1.2, 1.5, 5.0, 2.5, 1.0)] double x)
{
var n = new InverseGamma(a, b);
if (x >= 0)
{
Assert.AreEqual(Math.Pow(b, a) * Math.Pow(x, -a - 1.0) * Math.Exp(-b / x) / SpecialFunctions.Gamma(a), n.Density(x));
}
else
{
Assert.AreEqual(0.0, n.Density(x));
}
}
public void SetAFailsWithNonPositiveA(double a)
{
var n = new InverseGamma(1.0, 1.0);
Assert.Throws<ArgumentOutOfRangeException>(() => n.Shape = a);
}
public void CanCreateInverseGamma(double a, double b)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(a, n.Shape);
Assert.AreEqual(b, n.Scale);
}
public void ValidateCumulativeDistribution(double a, double b, double x)
{
var n = new InverseGamma(a, b);
Assert.AreEqual<double>(SpecialFunctions.GammaLowerIncomplete(a, b / x), n.CumulativeDistribution(x));
}
public void CanSetB(double b)
{
var n = new InverseGamma(1.0, 1.0);
n.Scale = b;
}
public void CanSampleSequence()
{
var n = new InverseGamma(1.0, 1.0);
var ied = n.Samples();
ied.Take(5).ToArray();
}
public void CanSample()
{
var n = new InverseGamma(1.0, 1.0);
n.Sample();
}
public void ValidateMedian()
{
var n = new InverseGamma(1.0, 1.0);
var median = n.Median;
}
public void ValidateMedianThrowsNotSupportedException()
{
var n = new InverseGamma(1.0, 1.0);
Assert.Throws <NotSupportedException>(() => { var median = n.Median; });
}
public void ValidateMaximum()
{
var n = new InverseGamma(1.0, 1.0);
Assert.AreEqual(Double.PositiveInfinity, n.Maximum);
}
public void ValidateToString()
{
var n = new InverseGamma(1.1d, 2.1d);
Assert.AreEqual("InverseGamma(α = 1.1, β = 2.1)", n.ToString());
}
public void SetBFailsWithNonPositiveB(double b)
{
var n = new InverseGamma(1.0, 1.0);
n.Scale = b;
}
public void ValidateToString()
{
var n = new InverseGamma(1.1, 2.1);
Assert.AreEqual(String.Format("InverseGamma(Shape = {0}, Inverse Scale = {1})", n.Shape, n.Scale), n.ToString());
}
public void InverseGammaCreateFailsWithBadParameters(double a, double b)
{
var n = new InverseGamma(a, b);
}
public void ValidateCumulativeDistribution(double a, double b, double x)
{
var n = new InverseGamma(a, b);
Assert.AreEqual <double>(SpecialFunctions.GammaUpperRegularized(a, b / x), n.CumulativeDistribution(x));
}
public void ValidateDensityLn(double a, double b, double x)
{
var n = new InverseGamma(a, b);
Assert.AreEqual <double>(Math.Log(n.Density(x)), n.DensityLn(x));
}
public void ValidateMedian()
{
var n = new InverseGamma(1.0, 1.0);
var median = n.Median;
}
public void ValidateMode(double a, double b)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(b / (a + 1.0), n.Mode);
}
public void ValidateMean(double a, double b)
{
var n = new InverseGamma(a, b);
if (a > 1)
{
Assert.AreEqual(b / (a - 1.0), n.Mean);
}
}
public void ValidateMinimum()
{
var n = new InverseGamma(1.0, 1.0);
Assert.AreEqual(0.0, n.Minimum);
}
public void ValidateStdDev(double a, double b)
{
var n = new InverseGamma(a, b);
if (a > 2)
{
Assert.AreEqual(b / ((a - 1.0) * Math.Sqrt(a - 2.0)), n.StdDev);
}
}
public void CanSetA(double a)
{
var n = new InverseGamma(1.0, 1.0);
n.Shape = a;
}
public void ValidateMedianThrowsNotSupportedException()
{
var n = new InverseGamma(1.0, 1.0);
Assert.Throws<NotSupportedException>(() => { var median = n.Median; });
}
public void ValidateToString()
{
var n = new InverseGamma(1.1, 2.1);
Assert.AreEqual<string>("InverseGamma(Shape = 1.1, Inverse Scale = 2.1)", n.ToString());
}
public void ValidateMaximum()
{
var n = new InverseGamma(1.0, 1.0);
Assert.AreEqual(Double.PositiveInfinity, n.Maximum);
}
public void CanSetA(double a)
{
var n = new InverseGamma(1.0, 1.0);
n.Shape = a;
}
public void ValidateDensityLn(double a, double b, double x)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(Math.Log(n.Density(x)), n.DensityLn(x));
}
public void ValidateMean([Values(0.1, 1.0, Double.PositiveInfinity)] double a, [Values(0.1, 1.0, Double.PositiveInfinity)] double b)
{
var n = new InverseGamma(a, b);
if (a > 1)
{
Assert.AreEqual(b / (a - 1.0), n.Mean);
}
}
public void ValidateVariance([Values(0.1, 1.0, Double.PositiveInfinity)] double a, [Values(0.1, 1.0, Double.PositiveInfinity)] double b)
{
var n = new InverseGamma(a, b);
if (a > 2)
{
Assert.AreEqual(b * b / ((a - 1.0) * (a - 1.0) * (a - 2.0)), n.Variance);
}
}
public void SetBFailsWithNonPositiveB(double b)
{
var n = new InverseGamma(1.0, 1.0);
Assert.Throws<ArgumentOutOfRangeException>(() => n.Scale = b);
}
public void ValidateStdDev([Values(0.1, 1.0, Double.PositiveInfinity)] double a, [Values(0.1, 1.0, Double.PositiveInfinity)] double b)
{
var n = new InverseGamma(a, b);
if (a > 2)
{
Assert.AreEqual(b / ((a - 1.0) * Math.Sqrt(a - 2.0)), n.StdDev);
}
}
public void ValidateVariance(double a, double b)
{
var n = new InverseGamma(a, b);
if (a > 2)
{
Assert.AreEqual(b * b / ((a - 1.0) * (a - 1.0) * (a - 2.0)), n.Variance);
}
}
public void ValidateMode([Values(0.1, 1.0, Double.PositiveInfinity)] double a, [Values(0.1, 1.0, Double.PositiveInfinity)] double b)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(b / (a + 1.0), n.Mode);
}
public void ValidateMode(double a, double b)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(b / (a + 1.0), n.Mode);
}
public void ValidateDensity(
[Values(0.1, 0.1, 0.1, 1.0, 1.0, 1.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double a,
[Values(0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity)] double b,
[Values(1.2, 2.0, 1.1, 1.5, 1.2, 1.5, 5.0, 2.5, 1.0)] double x)
{
var n = new InverseGamma(a, b);
if (x >= 0)
{
Assert.AreEqual(Math.Pow(b, a) * Math.Pow(x, -a - 1.0) * Math.Exp(-b / x) / SpecialFunctions.Gamma(a), n.Density(x));
}
else
{
Assert.AreEqual(0.0, n.Density(x));
}
}
public void ValidateMinimum()
{
var n = new InverseGamma(1.0, 1.0);
Assert.AreEqual(0.0, n.Minimum);
}
public void ValidateDensityLn(
[Values(0.1, 0.1, 0.1, 1.0, 1.0, 1.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double a,
[Values(0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity)] double b,
[Values(1.2, 2.0, 1.1, 1.5, 1.2, 1.5, 5.0, 2.5, 1.0)] double x)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(Math.Log(n.Density(x)), n.DensityLn(x));
}
public void ValidateDensity(double a, double b, double x)
{
var n = new InverseGamma(a, b);
if (x >= 0)
{
Assert.AreEqual(Math.Pow(b, a) * Math.Pow(x, -a - 1.0) * Math.Exp(-b / x) / SpecialFunctions.Gamma(a), n.Density(x));
}
else
{
Assert.AreEqual(0.0, n.Density(x));
}
}
public void ValidateCumulativeDistribution(
[Values(0.1, 0.1, 0.1, 1.0, 1.0, 1.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double a,
[Values(0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity, 0.1, 1.0, Double.PositiveInfinity)] double b,
[Values(1.2, 2.0, 1.1, 1.5, 1.2, 1.5, 5.0, 2.5, 1.0)] double x)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(SpecialFunctions.GammaUpperRegularized(a, b / x), n.CumulativeDistribution(x));
}
public void CanSample()
{
var n = new InverseGamma(1.0, 1.0);
n.Sample();
}
public void CanCreateInverseGamma([Values(0.1, 1.0, Double.PositiveInfinity)] double a, [Values(0.1, 1.0, Double.PositiveInfinity)] double b)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(a, n.Shape);
Assert.AreEqual(b, n.Scale);
}
public void ValidateCumulativeDistribution(double a, double b, double x)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(SpecialFunctions.GammaUpperRegularized(a, b / x), n.CumulativeDistribution(x));
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Inverse-gamma_distribution">InverseGamma distribution</a>
public void Run()
{
// 1. Initialize the new instance of the InverseGamma distribution class with parameters shape = 4, scale = 0.5
var inverseGamma = new InverseGamma(4, 0.5);
Console.WriteLine(@"1. Initialize the new instance of the InverseGamma distribution class with parameters Shape = {0}, Scale = {1}", inverseGamma.Shape, inverseGamma.Scale);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", inverseGamma);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", inverseGamma.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", inverseGamma.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", inverseGamma.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", inverseGamma.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", inverseGamma.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", inverseGamma.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", inverseGamma.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", inverseGamma.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", inverseGamma.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", inverseGamma.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", inverseGamma.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the InverseGamma distribution
Console.WriteLine(@"3. Generate 10 samples of the InverseGamma distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(inverseGamma.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the InverseGamma(4, 0.5) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the InverseGamma(4, 0.5) distribution and display histogram");
var data = new double[100000];
InverseGamma.Samples(data, 4, 0.5);
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the InverseGamma(8, 0.5) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the InverseGamma(8, 0.5) distribution and display histogram");
InverseGamma.Samples(data, 8, 0.5);
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the InverseGamma(2, 1) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the InverseGamma(8, 2) distribution and display histogram");
InverseGamma.Samples(data, 8, 2);
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateToString()
{
var n = new InverseGamma(1.1, 2.1);
Assert.AreEqual(String.Format("InverseGamma(Shape = {0}, Inverse Scale = {1})", n.Shape, n.Scale), n.ToString());
}
public void SetBFailsWithNonPositiveB(double b)
{
var n = new InverseGamma(1.0, 1.0);
n.Scale = b;
}