/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Zipf_distribution">Zipf distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Zipf distribution class with parameters S = 5, N = 10
var zipf = new Zipf(5, 10);
Console.WriteLine(@"1. Initialize the new instance of the Zipf distribution class with parameters S = {0}, N = {1}", zipf.S, zipf.N);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", zipf);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '3'", zipf.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability mass at location '3'", zipf.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability mass at location '3'", zipf.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", zipf.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", zipf.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", zipf.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", zipf.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", zipf.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", zipf.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", zipf.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", zipf.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the Zipf distribution
Console.WriteLine(@"3. Generate 10 samples of the Zipf distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(zipf.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Zipf(5, 10) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Zipf(5, 10) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = zipf.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Zipf(2, 10) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Zipf(2, 10) distribution and display histogram");
zipf.S = 2;
for (var i = 0; i < data.Length; i++)
{
data[i] = zipf.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the Zipf(5, 20) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the Zipf(1, 20) distribution and display histogram");
zipf.S = 1;
zipf.N = 20;
for (var i = 0; i < data.Length; i++)
{
data[i] = zipf.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateCumulativeDistribution(double s, int n, int x)
{
var d = new Zipf(s, n);
var cdf = SpecialFunctions.GeneralHarmonic(x, s) / SpecialFunctions.GeneralHarmonic(n, s);
AssertHelpers.AlmostEqualRelative(cdf, d.CumulativeDistribution(x), 14);
}