public void ValidateToString()
{
var n = new Rayleigh(2d);
Assert.AreEqual("Rayleigh(σ = 2)", n.ToString());
}
public void ValidateVariance(double scale)
{
var n = new Rayleigh(scale);
Assert.AreEqual((2.0 - Constants.PiOver2) * scale * scale, n.Variance);
}
public void ValidateSkewness(double scale, double skn)
{
var n = new Rayleigh(scale);
AssertHelpers.AlmostEqualRelative(skn, n.Skewness, 17);
}
public void ValidateStdDev(double scale)
{
var n = new Rayleigh(scale);
Assert.AreEqual(Math.Sqrt(2.0 - Constants.PiOver2) * scale, n.StdDev);
}
public void SetScaleFailsWithNegativeScale(double scale)
{
var n = new Rayleigh(1.0);
Assert.Throws<ArgumentOutOfRangeException>(() => n.Scale = scale);
}
public void ValidateMode(double scale)
{
var n = new Rayleigh(scale);
Assert.AreEqual(scale, n.Mode);
}
public void ValidateMean(double scale)
{
var n = new Rayleigh(scale);
Assert.AreEqual(scale * Math.Sqrt(Constants.PiOver2), n.Mean);
}
public void CanSampleSequence()
{
var n = new Rayleigh(1.0);
var ied = n.Samples();
ied.Take(5).ToArray();
}
public void ValidateInverseCumulativeDistribution(double scale, double x)
{
var n = new Rayleigh(scale);
double cdf = 1.0 - Math.Exp(-x*x/(2.0*scale*scale));
Assert.AreEqual(x, n.InverseCumulativeDistribution(cdf));
Assert.AreEqual(x, Rayleigh.InvCDF(scale, cdf));
}
public void ValidateMaximum(double scale)
{
var n = new Rayleigh(1.0);
Assert.AreEqual(Double.PositiveInfinity, n.Maximum);
}
public void ValidateEntropy(double scale)
{
var n = new Rayleigh(scale);
Assert.AreEqual(1.0 + Math.Log(scale / Constants.Sqrt2) + (Constants.EulerMascheroni / 2.0), n.Entropy);
}
public void ValidateDensityLn(double scale, double x)
{
var n = new Rayleigh(scale);
double expected = Math.Log(x/(scale*scale)) - (x*(x/(2.0*(scale*scale))));
Assert.AreEqual(expected, n.DensityLn(x));
Assert.AreEqual(expected, Rayleigh.PDFLn(scale, x));
}
public void ValidateDensity(double scale, double x)
{
var n = new Rayleigh(scale);
double expected = (x/(scale*scale))*Math.Exp(-x*x/(2.0*scale*scale));
Assert.AreEqual(expected, n.Density(x));
Assert.AreEqual(expected, Rayleigh.PDF(scale, x));
}
public void CanCreateRayleigh(double scale)
{
var n = new Rayleigh(scale);
Assert.AreEqual(scale, n.Scale);
}
public void ValidateMedian(double scale)
{
var n = new Rayleigh(scale);
Assert.AreEqual(scale * Math.Sqrt(Math.Log(4.0)), n.Median);
}
public void CanSample()
{
var n = new Rayleigh(1.0);
n.Sample();
}
public void ValidateMinimum(double scale)
{
var n = new Rayleigh(scale);
Assert.AreEqual(0.0, n.Minimum);
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Rayleigh_distribution">Rayleigh distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Rayleigh distribution class with parameter Scale = 1.
var rayleigh = new Rayleigh(1);
Console.WriteLine(@"1. Initialize the new instance of the Rayleigh distribution class with parameter Scale = {0}", rayleigh.Scale);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", rayleigh);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", rayleigh.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", rayleigh.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", rayleigh.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", rayleigh.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", rayleigh.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", rayleigh.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", rayleigh.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", rayleigh.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", rayleigh.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", rayleigh.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", rayleigh.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", rayleigh.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the Rayleigh distribution
Console.WriteLine(@"3. Generate 10 samples of the Rayleigh distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(rayleigh.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Rayleigh(1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Rayleigh(1) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = rayleigh.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Rayleigh(4) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Rayleigh(4) distribution and display histogram");
rayleigh.Scale = 4;
for (var i = 0; i < data.Length; i++)
{
data[i] = rayleigh.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the Rayleigh(0.5) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the Rayleigh(0.5) distribution and display histogram");
rayleigh.Scale = 0.5;
for (var i = 0; i < data.Length; i++)
{
data[i] = rayleigh.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void SetScaleFailsWithNegativeScale(double scale)
{
var n = new Rayleigh(1.0);
Assert.That(() => n.Scale = scale, Throws.ArgumentException);
}