/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Stable_distribution">Stable distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Stable distribution class with parameters Alpha = 2.0, Beta = 0, Scale = 1, Location = 0.
var stable = new Stable(2.0, 0, 1, 0);
Console.WriteLine(@"1. Initialize the new instance of the Stable distribution class with parameters Alpha = {0}, Beta = {1}, Scale = {2}, Location = {3}", stable.Alpha, stable.Beta, stable.Scale, stable.Location);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", stable);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", stable.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", stable.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", stable.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", stable.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", stable.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", stable.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", stable.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", stable.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", stable.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", stable.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", stable.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the Stable distribution
Console.WriteLine(@"3. Generate 10 samples of the Stable distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(stable.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Stable(1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Stable(2, 0, 1, 0) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = stable.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Stable(1, 0, 1, 0) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Stable(1, 0, 1, 0) distribution and display histogram");
stable.Alpha = 1;
for (var i = 0; i < data.Length; i++)
{
data[i] = stable.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the Stable(1.5, 1, 1, 5) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the Stable(1.5, 1, 1, 5) distribution and display histogram");
stable.Alpha = 1.5;
stable.Beta = 1;
stable.Location = 5;
stable.Scale = 5;
for (var i = 0; i < data.Length; i++)
{
data[i] = stable.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateCumulativeDistribution(double alpha, double beta, double scale, double location, double x, double cdf)
{
var n = new Stable(alpha, beta, scale, location);
AssertHelpers.AlmostEqualRelative(cdf, n.CumulativeDistribution(x), 15);
}