public void ValidateCumulativeDistribution(double location, double scale) { var n = new Cauchy(location, scale); for (var i = 0; i < 11; i++) { var x = i - 5.0; double expected = (Math.Atan((x - location) / scale)) / Math.PI + 0.5; Assert.AreEqual(expected, n.CumulativeDistribution(x), 1e-12); Assert.AreEqual(expected, Cauchy.CDF(location, scale, x), 1e-12); } }
/// <summary> /// Run example /// </summary> /// <a href="http://en.wikipedia.org/wiki/Cauchy_distribution">Cauchy distribution</a> public void Run() { // 1. Initialize the new instance of the Cauchy distribution class with parameters Location = 1 and Scale = 2. var cauchy = new Cauchy(1, 2); Console.WriteLine(@"1. Initialize the new instance of the Cauchy distribution class with parameters Location = {0} and Scale = {1}", cauchy.Location, cauchy.Scale); Console.WriteLine(); // 2. Distributuion properties: Console.WriteLine(@"2. {0} distributuion properties:", cauchy); // Cumulative distribution function Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", cauchy.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000")); // Probability density Console.WriteLine(@"{0} - Probability density at location '0.3'", cauchy.Density(0.3).ToString(" #0.00000;-#0.00000")); // Log probability density Console.WriteLine(@"{0} - Log probability density at location '0.3'", cauchy.DensityLn(0.3).ToString(" #0.00000;-#0.00000")); // Entropy Console.WriteLine(@"{0} - Entropy", cauchy.Entropy.ToString(" #0.00000;-#0.00000")); // Largest element in the domain Console.WriteLine(@"{0} - Largest element in the domain", cauchy.Maximum.ToString(" #0.00000;-#0.00000")); // Smallest element in the domain Console.WriteLine(@"{0} - Smallest element in the domain", cauchy.Minimum.ToString(" #0.00000;-#0.00000")); // Median Console.WriteLine(@"{0} - Median", cauchy.Median.ToString(" #0.00000;-#0.00000")); // Mode Console.WriteLine(@"{0} - Mode", cauchy.Mode.ToString(" #0.00000;-#0.00000")); // 3. Generate 10 samples of the Cauchy distribution Console.WriteLine(@"3. Generate 10 samples of the Cauchy distribution"); for (var i = 0; i < 10; i++) { Console.Write(cauchy.Sample().ToString("N05") + @" "); } Console.WriteLine(); }
public void ValidateCumulativeDistribution([Values(0.0, 0.0, 0.0, -5.0, 0.0)] double location, [Values(0.1, 1.0, 10.0, 100.0, Double.PositiveInfinity)] double scale) { var n = new Cauchy(location, scale); for (var i = 0; i < 11; i++) { var x = i - 5.0; Assert.AreEqual(((1.0 / Constants.Pi) * Math.Atan((x - location) / scale)) + 0.5, n.CumulativeDistribution(x)); } }
public void ValidateCumulativeDistribution(double location, double scale) { var n = new Cauchy(location, scale); for (var i = 0; i < 11; i++) { var x = i - 5.0; Assert.AreEqual(((1.0 / Constants.Pi) * Math.Atan((x - location) / scale)) + 0.5, n.CumulativeDistribution(x)); } }