Example #1
1
        /// <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();
        }
Example #2
0
        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);
 }
Example #7
0
 /// <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);
 }
Example #14
0
        /// <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);
        }