/// <summary> /// Run example /// </summary> public void Run() { // 1. Get 10 random samples of f(x) = (x * x) / 2 using continuous uniform distribution on [-10, 10] var uniform = new ContinuousUniform(-10, 10); var result = Generate.RandomMap(10, uniform, Function); Console.WriteLine(@" 1. Get 10 random samples of f(x) = (x * x) / 2 using continuous uniform distribution on [-10, 10]"); for (var i = 0; i < result.Length; i++) { Console.Write(result[i].ToString("N") + @" "); } Console.WriteLine(); Console.WriteLine(); // 2. Get 10 random samples of f(x) = (x * x) / 2 using Exponential(1) distribution and retrieve sample points var exponential = new Exponential(1); double[] samplePoints = Generate.Random(10, exponential); result = Generate.Map(samplePoints, Function); Console.WriteLine(@"2. Get 10 random samples of f(x) = (x * x) / 2 using Exponential(1) distribution and retrieve sample points"); Console.Write(@"Points: "); for (var i = 0; i < samplePoints.Length; i++) { Console.Write(samplePoints[i].ToString("N") + @" "); } Console.WriteLine(); Console.Write(@"Values: "); for (var i = 0; i < result.Length; i++) { Console.Write(result[i].ToString("N") + @" "); } Console.WriteLine(); Console.WriteLine(); // 3. Get 10 random samples of f(x, y) = (x * y) / 2 using ChiSquare(10) distribution var chiSquare = new ChiSquared(10); result = Generate.RandomMap2(10, chiSquare, TwoDomainFunction); Console.WriteLine(@" 3. Get 10 random samples of f(x, y) = (x * y) / 2 using ChiSquare(10) distribution"); for (var i = 0; i < result.Length; i++) { Console.Write(result[i].ToString("N") + @" "); } Console.WriteLine(); }
static void SamplesUnchecked(System.Random rnd, double[] values, double d1, double d2) { var values2 = new double[values.Length]; ChiSquared.SamplesUnchecked(rnd, values, d1); ChiSquared.SamplesUnchecked(rnd, values2, d2); CommonParallel.For(0, values.Length, 4096, (a, b) => { for (int i = a; i < b; i++) { values[i] = (values[i] * d2) / (values2[i] * d1); } }); }
public void ValidateDensityLn(double dof, double x, double expected) { var chiSquared = new ChiSquared(dof); Assert.That(chiSquared.DensityLn(x), Is.EqualTo(expected).Within(13)); Assert.That(ChiSquared.PDFLn(dof, x), Is.EqualTo(expected).Within(13)); }
public void ValidateMaximum() { var n = new ChiSquared(1.0); Assert.AreEqual(Double.PositiveInfinity, n.Maximum); }
public void ValidateMinimum() { var n = new ChiSquared(1.0); Assert.AreEqual(0.0, n.Minimum); }
public void SetDofFailsWithNonPositiveDoF(double dof) { var n = new ChiSquared(1.0); Assert.Throws<ArgumentOutOfRangeException>(() => n.DegreesOfFreedom = dof); }
/// <summary> /// Generates one sample from the <c>FisherSnedecor</c> distribution without parameter checking. /// </summary> /// <param name="rnd">The random number generator to use.</param> /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param> /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param> /// <returns>a <c>FisherSnedecor</c> distributed random number.</returns> static double SampleUnchecked(System.Random rnd, double d1, double d2) { return((ChiSquared.Sample(rnd, d1) * d2) / (ChiSquared.Sample(rnd, d2) * d1)); }
public void ValidateToString() { var n = new ChiSquared(1.0); Assert.AreEqual("ChiSquared(k = 1)", n.ToString()); }
public void ValidateInverseCumulativeDistribution(double dof, double x, double expected) { var chiSquared = new ChiSquared(dof); Assert.That(chiSquared.InverseCumulativeDistribution(x), Is.EqualTo(expected).Within(1e-14)); Assert.That(ChiSquared.InvCDF(dof, x), Is.EqualTo(expected).Within(1e-14)); }
public void ValidateDensityLn(double dof, double x) { var n = new ChiSquared(dof); double expected = (-x / 2.0) + (((dof / 2.0) - 1.0) * Math.Log(x)) - ((dof / 2.0) * Math.Log(2)) - SpecialFunctions.GammaLn(dof / 2.0); Assert.AreEqual(expected, n.DensityLn(x)); Assert.AreEqual(expected, ChiSquared.PDFLn(dof, x)); }
public void ValidateDensity(double dof, double x) { var n = new ChiSquared(dof); double expected = (Math.Pow(x, (dof / 2.0) - 1.0) * Math.Exp(-x / 2.0)) / (Math.Pow(2.0, dof / 2.0) * SpecialFunctions.Gamma(dof / 2.0)); Assert.AreEqual(expected, n.Density(x)); Assert.AreEqual(expected, ChiSquared.PDF(dof, x)); }
public void ValidateCumulativeDistribution(double dof, double x) { var n = new ChiSquared(dof); double expected = SpecialFunctions.GammaLowerIncomplete(dof / 2.0, x / 2.0) / SpecialFunctions.Gamma(dof / 2.0); Assert.AreEqual(expected, n.CumulativeDistribution(x)); Assert.AreEqual(expected, ChiSquared.CDF(dof, x)); }
public void SetDofFailsWithNonPositiveDoF(double dof) { var n = new ChiSquared(1.0); Assert.That(() => n.DegreesOfFreedom = dof, Throws.ArgumentException); }
/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient">Pearson product-moment correlation coefficient</seealso> public void Run() { // 1. Initialize the new instance of the ChiSquare distribution class with parameter dof = 5. var chiSquare = new ChiSquared(5); Console.WriteLine(@"1. Initialize the new instance of the ChiSquare distribution class with parameter DegreesOfFreedom = {0}", chiSquare.DegreesOfFreedom); Console.WriteLine(@"{0} distributuion properties:", chiSquare); Console.WriteLine(@"{0} - Largest element", chiSquare.Maximum.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Smallest element", chiSquare.Minimum.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Mean", chiSquare.Mean.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Median", chiSquare.Median.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Mode", chiSquare.Mode.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Variance", chiSquare.Variance.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Standard deviation", chiSquare.StdDev.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Skewness", chiSquare.Skewness.ToString(" #0.00000;-#0.00000")); Console.WriteLine(); // 2. Generate 1000 samples of the ChiSquare(5) distribution Console.WriteLine(@"2. Generate 1000 samples of the ChiSquare(5) distribution"); var data = new double[1000]; for (var i = 0; i < data.Length; i++) { data[i] = chiSquare.Sample(); } // 3. Get basic statistics on set of generated data using extention methods Console.WriteLine(@"3. Get basic statistics on set of generated data using extention methods"); Console.WriteLine(@"{0} - Largest element", data.Maximum().ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Smallest element", data.Minimum().ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Mean", data.Mean().ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Median", data.Median().ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Biased population variance", data.PopulationVariance().ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Variance", data.Variance().ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Standard deviation", data.StandardDeviation().ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Biased sample standard deviation", data.PopulationStandardDeviation().ToString(" #0.00000;-#0.00000")); Console.WriteLine(); // 4. Compute the basic statistics of data set using DescriptiveStatistics class Console.WriteLine(@"4. Compute the basic statistics of data set using DescriptiveStatistics class"); var descriptiveStatistics = new DescriptiveStatistics(data); Console.WriteLine(@"{0} - Kurtosis", descriptiveStatistics.Kurtosis.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Largest element", descriptiveStatistics.Maximum.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Smallest element", descriptiveStatistics.Minimum.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Mean", descriptiveStatistics.Mean.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Variance", descriptiveStatistics.Variance.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Standard deviation", descriptiveStatistics.StandardDeviation.ToString(" #0.00000;-#0.00000")); Console.WriteLine(@"{0} - Skewness", descriptiveStatistics.Skewness.ToString(" #0.00000;-#0.00000")); Console.WriteLine(); // Generate 1000 samples of the ChiSquare(2.5) distribution var chiSquareB = new ChiSquared(2); var dataB = new double[1000]; for (var i = 0; i < data.Length; i++) { dataB[i] = chiSquareB.Sample(); } // 5. Correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5) Console.WriteLine(@"5. Correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5) is {0}", Correlation.Pearson(data, dataB).ToString("N04")); Console.WriteLine(@"6. Ranked correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5) is {0}", Correlation.Spearman(data, dataB).ToString("N04")); Console.WriteLine(); // 6. Correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x data = Generate.LinearSpacedMap(1000, 0, 100, x => x * 2); dataB = Generate.LinearSpacedMap(1000, 0, 100, x => x * x); Console.WriteLine(@"7. Correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x is {0}", Correlation.Pearson(data, dataB).ToString("N04")); Console.WriteLine(@"8. Ranked correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x is {0}", Correlation.Spearman(data, dataB).ToString("N04")); Console.WriteLine(); }
public void CanSample() { var n = new ChiSquared(1.0); n.Sample(); }
public void CanSampleSequence() { var n = new ChiSquared(1.0); var ied = n.Samples(); GC.KeepAlive(ied.Take(5).ToArray()); }
public void ValidateVariance(double dof) { var n = new ChiSquared(dof); Assert.AreEqual(2 * dof, n.Variance); }
public void CanCreateChiSquare(double dof) { var n = new ChiSquared(dof); Assert.AreEqual(dof, n.DegreesOfFreedom); }
public void ValidateStdDev(double dof) { var n = new ChiSquared(dof); Assert.AreEqual(Math.Sqrt(n.Variance), n.StdDev); }
public void ValidateMean(double dof) { var n = new ChiSquared(dof); Assert.AreEqual(dof, n.Mean); }
public void ValidateMode(double dof) { var n = new ChiSquared(dof); Assert.AreEqual(dof - 2, n.Mode); }
public void ValidateMedian(double dof) { var n = new ChiSquared(dof); Assert.AreEqual(dof - (2.0 / 3.0), n.Median); }
/// <summary> /// Run example /// </summary> /// <a href="http://en.wikipedia.org/wiki/Chi-square_distribution">ChiSquare distribution</a> public void Run() { // 1. Initialize the new instance of the ChiSquare distribution class with parameter dof = 1. var chiSquare = new ChiSquared(1); Console.WriteLine(@"1. Initialize the new instance of the ChiSquare distribution class with parameter DegreesOfFreedom = {0}", chiSquare.DegreesOfFreedom); Console.WriteLine(); // 2. Distributuion properties: Console.WriteLine(@"2. {0} distributuion properties:", chiSquare); // Cumulative distribution function Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", chiSquare.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000")); // Probability density Console.WriteLine(@"{0} - Probability density at location '0.3'", chiSquare.Density(0.3).ToString(" #0.00000;-#0.00000")); // Log probability density Console.WriteLine(@"{0} - Log probability density at location '0.3'", chiSquare.DensityLn(0.3).ToString(" #0.00000;-#0.00000")); // Entropy Console.WriteLine(@"{0} - Entropy", chiSquare.Entropy.ToString(" #0.00000;-#0.00000")); // Largest element in the domain Console.WriteLine(@"{0} - Largest element in the domain", chiSquare.Maximum.ToString(" #0.00000;-#0.00000")); // Smallest element in the domain Console.WriteLine(@"{0} - Smallest element in the domain", chiSquare.Minimum.ToString(" #0.00000;-#0.00000")); // Mean Console.WriteLine(@"{0} - Mean", chiSquare.Mean.ToString(" #0.00000;-#0.00000")); // Median Console.WriteLine(@"{0} - Median", chiSquare.Median.ToString(" #0.00000;-#0.00000")); // Mode Console.WriteLine(@"{0} - Mode", chiSquare.Mode.ToString(" #0.00000;-#0.00000")); // Variance Console.WriteLine(@"{0} - Variance", chiSquare.Variance.ToString(" #0.00000;-#0.00000")); // Standard deviation Console.WriteLine(@"{0} - Standard deviation", chiSquare.StdDev.ToString(" #0.00000;-#0.00000")); // Skewness Console.WriteLine(@"{0} - Skewness", chiSquare.Skewness.ToString(" #0.00000;-#0.00000")); Console.WriteLine(); // 3. Generate 10 samples of the ChiSquare distribution Console.WriteLine(@"3. Generate 10 samples of the ChiSquare distribution"); for (var i = 0; i < 10; i++) { Console.Write(chiSquare.Sample().ToString("N05") + @" "); } Console.WriteLine(); Console.WriteLine(); // 4. Generate 100000 samples of the ChiSquare(1) distribution and display histogram Console.WriteLine(@"4. Generate 100000 samples of the ChiSquare(1) distribution and display histogram"); var data = new double[100000]; for (var i = 0; i < data.Length; i++) { data[i] = chiSquare.Sample(); } ConsoleHelper.DisplayHistogram(data); Console.WriteLine(); // 5. Generate 100000 samples of the ChiSquare(4) distribution and display histogram Console.WriteLine(@"5. Generate 100000 samples of the ChiSquare(4) distribution and display histogram"); chiSquare.DegreesOfFreedom = 4; for (var i = 0; i < data.Length; i++) { data[i] = chiSquare.Sample(); } ConsoleHelper.DisplayHistogram(data); Console.WriteLine(); // 6. Generate 100000 samples of the ChiSquare(8) distribution and display histogram Console.WriteLine(@"6. Generate 100000 samples of the ChiSquare(8) distribution and display histogram"); chiSquare.DegreesOfFreedom = 8; for (var i = 0; i < data.Length; i++) { data[i] = chiSquare.Sample(); } ConsoleHelper.DisplayHistogram(data); }