public override double Test(IList <IList <double> > samples)
{
double total_count = ToolsCollection.CountElements(samples);
double pooled_mean = ToolsMathStatistics.MeanAll(samples);
double nominator_part = 0.0;
double denominator_part = 0.0;
for (int sample_index = 0; sample_index < samples.Count; sample_index++)
{
double sample_mean = ToolsMathStatistics.Mean(samples[sample_index]);
double sample_median = ToolsMathStatistics.Quantile(samples[sample_index], 0.5f);
nominator_part += (sample_mean - pooled_mean) * (sample_mean - pooled_mean) * samples[sample_index].Count;
for (int measurement_index = 0; measurement_index < samples[sample_index].Count; measurement_index++)
{
double diff = Math.Abs(sample_median - samples[sample_index][measurement_index]) - sample_mean; //This is the difference with brown forsythe test
denominator_part += diff * diff;
}
}
double degrees_of_freedom_0 = samples.Count - 1;
double degrees_of_freedom_1 = total_count - samples.Count;
double f_statistic = (degrees_of_freedom_1 * nominator_part) / (degrees_of_freedom_0 * denominator_part);
FisherSnedecor distribution = new FisherSnedecor(degrees_of_freedom_0, degrees_of_freedom_1, new Random());
return(distribution.CumulativeDistribution(f_statistic));
}
public void ValidateCumulativeDistribution(double d1, double d2, double x)
{
var n = new FisherSnedecor(d1, d2);
double expected = SpecialFunctions.BetaRegularized(d1 / 2.0, d2 / 2.0, d1 * x / (d2 + (x * d1)));
Assert.That(n.CumulativeDistribution(x), Is.EqualTo(expected));
Assert.That(FisherSnedecor.CDF(d1, d2, x), Is.EqualTo(expected));
}
public void ValidateCumulativeDistribution(
[Values(0.1, 1.0, 10.0, 0.1, 1.0, 10.0, 0.1, 1.0, 10.0, 0.1, 1.0, 10.0)] double d1,
[Values(0.1, 0.1, 0.1, 1.0, 1.0, 1.0, 0.1, 0.1, 0.1, 1.0, 1.0, 1.0)] double d2,
[Values(1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0)] double x)
{
var n = new FisherSnedecor(d1, d2);
Assert.AreEqual(SpecialFunctions.BetaRegularized(d1 / 2.0, d2 / 2.0, d1 * x / (d2 + (x * d1))), n.CumulativeDistribution(x));
}
public void ValidateCumulativeDistribution(
[Values(0.1, 1.0, 10.0, 0.1, 1.0, 10.0, 0.1, 1.0, 10.0, 0.1, 1.0, 10.0)] double d1,
[Values(0.1, 0.1, 0.1, 1.0, 1.0, 1.0, 0.1, 0.1, 0.1, 1.0, 1.0, 1.0)] double d2,
[Values(1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0)] double x)
{
var n = new FisherSnedecor(d1, d2);
Assert.AreEqual(SpecialFunctions.BetaRegularized(d1 / 2.0, d2 / 2.0, d1 * x / (d2 + (x * d1))), n.CumulativeDistribution(x));
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/F-distribution">FisherSnedecor distribution</a>
public void Run()
{
// 1. Initialize the new instance of the FisherSnedecor distribution class with parameter DegreeOfFreedom1 = 50, DegreeOfFreedom2 = 20.
var fisherSnedecor = new FisherSnedecor(50, 20);
Console.WriteLine(@"1. Initialize the new instance of the FisherSnedecor distribution class with parameters DegreeOfFreedom1 = {0}, DegreeOfFreedom2 = {1}", fisherSnedecor.DegreeOfFreedom1, fisherSnedecor.DegreeOfFreedom2);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", fisherSnedecor);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", fisherSnedecor.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", fisherSnedecor.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", fisherSnedecor.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", fisherSnedecor.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", fisherSnedecor.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", fisherSnedecor.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", fisherSnedecor.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", fisherSnedecor.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", fisherSnedecor.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", fisherSnedecor.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the FisherSnedecor distribution
Console.WriteLine(@"3. Generate 10 samples of the FisherSnedecor distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(fisherSnedecor.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the FisherSnedecor(50, 20) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the FisherSnedecor(50, 20) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = fisherSnedecor.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the FisherSnedecor(20, 10) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the FisherSnedecor(20, 10) distribution and display histogram");
fisherSnedecor.DegreeOfFreedom1 = 20;
fisherSnedecor.DegreeOfFreedom2 = 10;
for (var i = 0; i < data.Length; i++)
{
data[i] = fisherSnedecor.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the FisherSnedecor(100, 100) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the FisherSnedecor(100, 100) distribution and display histogram");
fisherSnedecor.DegreeOfFreedom1 = 100;
fisherSnedecor.DegreeOfFreedom2 = 100;
for (var i = 0; i < data.Length; i++)
{
data[i] = fisherSnedecor.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateCumulativeDistribution(double d1, double d2, double x)
{
var n = new FisherSnedecor(d1, d2);
Assert.AreEqual <double>(SpecialFunctions.BetaRegularized(d1 / 2.0, d2 / 2.0, d1 * x / (d2 + x * d1)), n.CumulativeDistribution(x));
}
public void ValidateCumulativeDistribution(double d1, double d2, double x)
{
var n = new FisherSnedecor(d1, d2);
Assert.AreEqual<double>(SpecialFunctions.BetaRegularized(d1 / 2.0, d2 / 2.0, d1 * d2 / (d1 + d1 * d2)), n.CumulativeDistribution(x));
}
