public void ValidateCumulativeDistribution(double scale, double shape, double x)
{
var n = new Pareto(scale, shape);
double expected = 1.0 - Math.Pow(scale/x, shape);
Assert.AreEqual(expected, n.CumulativeDistribution(x));
Assert.AreEqual(expected, Pareto.CDF(scale, shape, x));
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Pareto_distribution">Pareto distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Pareto distribution class with parameters Shape = 3, Scale = 1
var pareto = new Pareto(1, 3);
Console.WriteLine(@"1. Initialize the new instance of the Pareto distribution class with parameters Shape = {0}, Scale = {1}", pareto.Shape, pareto.Scale);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", pareto);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", pareto.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", pareto.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", pareto.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", pareto.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", pareto.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", pareto.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", pareto.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", pareto.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", pareto.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", pareto.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", pareto.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", pareto.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the Pareto distribution
Console.WriteLine(@"3. Generate 10 samples of the Pareto distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(pareto.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Pareto(1, 3) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Pareto(1, 3) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = pareto.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Pareto(1, 1) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Pareto(1, 1) distribution and display histogram");
pareto.Shape = 1;
for (var i = 0; i < data.Length; i++)
{
data[i] = pareto.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the Pareto(10, 5) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the Pareto(10, 50) distribution and display histogram");
pareto.Shape = 50;
pareto.Scale = 10;
for (var i = 0; i < data.Length; i++)
{
data[i] = pareto.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}