/// <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 ChiSquare(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 ChiSquare(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. Correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x
            data = SignalGenerator.EquidistantInterval(x => x * 2, 0, 100, 1000);
            dataB = SignalGenerator.EquidistantInterval(x => x * x, 0, 100, 1000);
            Console.WriteLine(@"6. 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();
        }
        /// <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 ChiSquare(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);
        }
Exemple #3
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 /// <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 parameter - degree of freedom.</param>
 /// <param name="d2">The second parameter - degree of freedom.</param>
 /// <returns>a <c>FisherSnedecor</c> distributed random number.</returns>
 internal static double SampleUnchecked(Random rnd, double d1, double d2)
 {
     return((ChiSquare.Sample(rnd, d1) / d1) / (ChiSquare.Sample(rnd, d2) / d2));
 }
Exemple #4
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        /// <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 = SignalGenerator.Random(Function, uniform, 10);
            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;
            result = SignalGenerator.Random(Function, exponential, 10, out samplePoints);
            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 ChiSquare(10);
            result = SignalGenerator.Random(TwoDomainFunction, chiSquare, 10);
            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();
        }
 /// <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 parameter - degree of freedom.</param>
 /// <param name="d2">The second parameter - degree of freedom.</param>
 /// <returns>a <c>FisherSnedecor</c> distributed random number.</returns>
 private static double DoSample(Random rnd, double d1, double d2)
 {
     return((ChiSquare.Sample(rnd, d1) / d1) / (ChiSquare.Sample(rnd, d2) / d2));
 }