/// <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 ValidateToString()
{
var d = new Zipf(1.0, 5);
Assert.AreEqual("Zipf(S = 1, N = 5)", d.ToString());
}
public void ValidateEntropy(double s, int n, double e)
{
var d = new Zipf(s, n);
AssertHelpers.AlmostEqualRelative(e, d.Entropy, 15);
}
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);
}
public void CanCreateZipf(double s, int n)
{
var d = new Zipf(s, n);
Assert.AreEqual(s, d.S);
Assert.AreEqual(n, d.N);
}
public void CanSample()
{
var d = new Zipf(0.7, 5);
var s = d.Sample();
Assert.LessOrEqual(s, 5);
Assert.GreaterOrEqual(s, 0);
}
public void CanSampleSequence()
{
var d = new Zipf(0.7, 5);
var ied = d.Samples();
var e = ied.Take(1000).ToArray();
foreach (var i in e)
{
Assert.LessOrEqual(i, 5);
Assert.GreaterOrEqual(i, 0);
}
}
public void ValidateProbability(double s, int n, int x)
{
var d = new Zipf(s, n);
Assert.AreEqual((1.0 / Math.Pow(x, s)) / SpecialFunctions.GeneralHarmonic(n, s), d.Probability(x));
}
public void ValidateProbabilityLn(double s, int n, int x)
{
var d = new Zipf(s, n);
Assert.AreEqual(Math.Log(d.Probability(x)), d.ProbabilityLn(x));
}
public void ValidateMaximum(double s, int n)
{
var d = new Zipf(s, n);
Assert.AreEqual(n, d.Maximum);
}
public void ValidateMinimum()
{
var d = new Zipf(1.0, 5);
Assert.AreEqual(1, d.Minimum);
}
public void ValidateMedianThrowsNotSupportedException()
{
var d = new Zipf(1.0, 5);
Assert.Throws<NotSupportedException>(() => { var m = d.Median; });
}
public void ValidateMode(double s, int n)
{
var d = new Zipf(s, n);
Assert.AreEqual(1, d.Mode);
}
public void ValidateSkewness(double s, int n)
{
var d = new Zipf(s, n);
if (s > 4)
{
Assert.AreEqual(((SpecialFunctions.GeneralHarmonic(n, s - 3) * Math.Pow(SpecialFunctions.GeneralHarmonic(n, s), 2)) - (SpecialFunctions.GeneralHarmonic(n, s - 1) * ((3 * SpecialFunctions.GeneralHarmonic(n, s - 2) * SpecialFunctions.GeneralHarmonic(n, s)) - Math.Pow(SpecialFunctions.GeneralHarmonic(n, s - 1), 2)))) / Math.Pow((SpecialFunctions.GeneralHarmonic(n, s - 2) * SpecialFunctions.GeneralHarmonic(n, s)) - Math.Pow(SpecialFunctions.GeneralHarmonic(n, s - 1), 2), 1.5), d.Skewness);
}
}