public void ValidateMode(double scale, double shape)
{
var n = new Pareto(scale, shape);
Assert.AreEqual(scale, n.Mode);
}
public void ValidateSkewness(double scale, double shape)
{
var n = new Pareto(scale, shape);
Assert.AreEqual((2.0 * (shape + 1.0) / (shape - 3.0)) * Math.Sqrt((shape - 2.0) / shape), n.Skewness);
}
public void ValidateMedian(double scale, double shape)
{
var n = new Pareto(scale, shape);
Assert.AreEqual(scale * Math.Pow(2.0, 1.0 / shape), n.Median);
}
public void ValidateMinimum(double scale)
{
var n = new Pareto(scale, 1.0);
Assert.AreEqual(scale, n.Minimum);
}
public void CanSample()
{
var n = new Pareto(1.0, 1.0);
n.Sample();
}
public void SetShapeFailsWithNegativeShape()
{
var n = new Pareto(1.0, 1.0);
Assert.Throws<ArgumentOutOfRangeException>(() => n.Shape = -1.0);
}
public void ValidateEntropy(double scale, double shape)
{
var n = new Pareto(scale, shape);
Assert.AreEqual(Math.Log(shape / scale) - (1.0 / shape) - 1.0, n.Entropy);
}
public void ValidateVariance(double scale, double shape)
{
var n = new Pareto(scale, shape);
if (shape <= 2.0)
{
Assert.AreEqual(double.PositiveInfinity, n.Variance);
}
else
{
Assert.AreEqual(scale * scale * shape / ((shape - 1.0) * (shape - 1.0) * (shape - 2.0)), n.Variance);
}
}
public void ValidateCumulativeDistribution(double scale, double shape, double x)
{
var n = new Pareto(scale, shape);
double expected = 1.0 - Math.Pow(scale/x, shape);
Assert.AreEqual(expected, n.CumulativeDistribution(x));
Assert.AreEqual(expected, Pareto.CDF(scale, shape, x));
}
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);
}
public void SetShapeFailsWithNegativeShape()
{
var n = new Pareto(1.0, 1.0);
Assert.That(() => n.Shape = -1.0, Throws.ArgumentException);
}
public void ParetoCreateFailsWithBadParameters(double scale, double shape)
{
Assert.That(() => { var n = new Pareto(scale, shape); }, Throws.ArgumentException);
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Pareto_distribution">Pareto distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Pareto distribution class with parameters Shape = 3, Scale = 1
var pareto = new Pareto(1, 3);
Console.WriteLine(@"1. Initialize the new instance of the Pareto distribution class with parameters Shape = {0}, Scale = {1}", pareto.Shape, pareto.Scale);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", pareto);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", pareto.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", pareto.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", pareto.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", pareto.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", pareto.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", pareto.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", pareto.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", pareto.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", pareto.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", pareto.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", pareto.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", pareto.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the Pareto distribution
Console.WriteLine(@"3. Generate 10 samples of the Pareto distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(pareto.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Pareto(1, 3) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Pareto(1, 3) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = pareto.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Pareto(1, 1) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Pareto(1, 1) distribution and display histogram");
pareto.Shape = 1;
for (var i = 0; i < data.Length; i++)
{
data[i] = pareto.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the Pareto(10, 5) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the Pareto(10, 50) distribution and display histogram");
pareto.Shape = 50;
pareto.Scale = 10;
for (var i = 0; i < data.Length; i++)
{
data[i] = pareto.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateStdDev(double scale, double shape)
{
var n = new Pareto(scale, shape);
Assert.AreEqual((scale * Math.Sqrt(shape)) / ((shape - 1.0) * Math.Sqrt(shape - 2.0)), n.StdDev);
}
public void ValidateInverseCumulativeDistribution(double scale, double shape, double x)
{
var n = new Pareto(scale, shape);
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);
}
public void ValidateToString()
{
var n = new Pareto(1d, 2d);
Assert.AreEqual("Pareto(xm = 1, α = 2)", n.ToString());
}
public void ValidateMaximum()
{
var n = new Pareto(1.0, 1.0);
Assert.AreEqual(Double.PositiveInfinity, n.Maximum);
}
public void CanCreatePareto(double scale, double shape)
{
var n = new Pareto(scale, shape);
Assert.AreEqual(scale, n.Scale);
Assert.AreEqual(shape, n.Shape);
}
public void ValidateMean(double scale, double shape)
{
var n = new Pareto(scale, shape);
if (shape > 1)
{
Assert.AreEqual(shape * scale / (shape - 1.0), n.Mean);
}
}
public void CanSampleSequence()
{
var n = new Pareto(1.0, 1.0);
var ied = n.Samples();
ied.Take(5).ToArray();
}
public void ParetoCreateFailsWithBadParameters(double scale, double shape)
{
Assert.Throws<ArgumentOutOfRangeException>(() => { var n = new Pareto(scale, shape); });
}