public void ValidateDensity(double dof, double x)
{
var n = new ChiSquared(dof);
double expected = (Math.Pow(x, (dof / 2.0) - 1.0) * Math.Exp(-x / 2.0)) / (Math.Pow(2.0, dof / 2.0) * SpecialFunctions.Gamma(dof / 2.0));
Assert.AreEqual(expected, n.Density(x));
Assert.AreEqual(expected, ChiSquared.PDF(dof, x));
}
public void ValidateDensity(double dof, double x, double expected)
{
var chiSquared = new ChiSquared(dof);
Assert.That(chiSquared.Density(x), Is.EqualTo(expected).Within(13));
Assert.That(ChiSquared.PDF(dof, x), Is.EqualTo(expected).Within(13));
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Chi-square_distribution">ChiSquare distribution</a>
public void Run()
{
// 1. Initialize the new instance of the ChiSquare distribution class with parameter dof = 1.
var chiSquare = new ChiSquared(1);
Console.WriteLine(@"1. Initialize the new instance of the ChiSquare distribution class with parameter DegreesOfFreedom = {0}", chiSquare.DegreesOfFreedom);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", chiSquare);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", chiSquare.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", chiSquare.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", chiSquare.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", chiSquare.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", chiSquare.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", chiSquare.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", chiSquare.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", chiSquare.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", chiSquare.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", chiSquare.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", chiSquare.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", chiSquare.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the ChiSquare distribution
Console.WriteLine(@"3. Generate 10 samples of the ChiSquare distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(chiSquare.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the ChiSquare(1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the ChiSquare(1) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = chiSquare.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the ChiSquare(4) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the ChiSquare(4) distribution and display histogram");
chiSquare.DegreesOfFreedom = 4;
for (var i = 0; i < data.Length; i++)
{
data[i] = chiSquare.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the ChiSquare(8) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the ChiSquare(8) distribution and display histogram");
chiSquare.DegreesOfFreedom = 8;
for (var i = 0; i < data.Length; i++)
{
data[i] = chiSquare.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
