/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/StudentT_distribution">StudentT distribution</a>
public void Run()
{
// 1. Initialize the new instance of the StudentT distribution class with parameters Location = 0, Scale = 1, DegreesOfFreedom = 1
var studentT = new StudentT();
Console.WriteLine(@"1. Initialize the new instance of the StudentT distribution class with parameters Location = {0}, Scale = {1}, DegreesOfFreedom = {2}", studentT.Location, studentT.Scale, studentT.DegreesOfFreedom);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", studentT);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", studentT.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", studentT.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", studentT.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", studentT.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", studentT.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", studentT.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", studentT.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", studentT.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", studentT.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", studentT.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", studentT.StdDev.ToString(" #0.00000;-#0.00000"));
// 3. Generate 10 samples of the StudentT distribution
Console.WriteLine(@"3. Generate 10 samples of the StudentT distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(studentT.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the StudentT(0, 1, 1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the StudentT(0, 1, 1) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = studentT.Sample();
}
ConsoleHelper.DisplayHistogram(data);
// 5. Generate 100000 samples of the StudentT(0, 1, 5) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the StudentT(0, 1, 5) distribution and display histogram");
studentT.DegreesOfFreedom = 5;
for (var i = 0; i < data.Length; i++)
{
data[i] = studentT.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the StudentT(0, 1, 10) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the StudentT(0, 1, 10) distribution and display histogram");
studentT.DegreesOfFreedom = 10;
for (var i = 0; i < data.Length; i++)
{
data[i] = studentT.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
/// <summary>
/// Density function for a Student's T distribution for a specified number
/// of degrees of freedom.
/// </summary>
public static double DT(double value, double df, double location = 0, double scale = 1)
{
var tdist = new StudentT(location, scale, df);
return tdist.Density(value);
}
public void ValidateDensity(double location, double scale, double dof, double x, double p)
{
var n = new StudentT(location, scale, dof);
AssertHelpers.AlmostEqualRelative(p, n.Density(x), 13);
}
