/// <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); } }