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