public void ValidateCumulativeDistribution(double d1, double d2, double x)
 {
     var n = new FisherSnedecor(d1, d2);
     double expected = SpecialFunctions.BetaRegularized(d1/2.0, d2/2.0, d1*x/(d2 + (x*d1)));
     Assert.That(n.CumulativeDistribution(x), Is.EqualTo(expected));
     Assert.That(FisherSnedecor.CDF(d1, d2, x), Is.EqualTo(expected));
 }
        /// <summary>
        /// Run example
        /// </summary>
        /// <a href="http://en.wikipedia.org/wiki/F-distribution">FisherSnedecor distribution</a>
        public void Run()
        {
            // 1. Initialize the new instance of the FisherSnedecor distribution class with parameter DegreesOfFreedom1 = 50, DegreesOfFreedom2 = 20.
            var fisherSnedecor = new FisherSnedecor(50, 20);
            Console.WriteLine(@"1. Initialize the new instance of the FisherSnedecor distribution class with parameters DegreesOfFreedom1 = {0}, DegreesOfFreedom2 = {1}", fisherSnedecor.DegreesOfFreedom1, fisherSnedecor.DegreesOfFreedom2);
            Console.WriteLine();

            // 2. Distributuion properties:
            Console.WriteLine(@"2. {0} distributuion properties:", fisherSnedecor);

            // Cumulative distribution function
            Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", fisherSnedecor.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));

            // Probability density
            Console.WriteLine(@"{0} - Probability density at location '0.3'", fisherSnedecor.Density(0.3).ToString(" #0.00000;-#0.00000"));

            // Log probability density
            Console.WriteLine(@"{0} - Log probability density at location '0.3'", fisherSnedecor.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));

            // Largest element in the domain
            Console.WriteLine(@"{0} - Largest element in the domain", fisherSnedecor.Maximum.ToString(" #0.00000;-#0.00000"));

            // Smallest element in the domain
            Console.WriteLine(@"{0} - Smallest element in the domain", fisherSnedecor.Minimum.ToString(" #0.00000;-#0.00000"));

            // Mean
            Console.WriteLine(@"{0} - Mean", fisherSnedecor.Mean.ToString(" #0.00000;-#0.00000"));

            // Mode
            Console.WriteLine(@"{0} - Mode", fisherSnedecor.Mode.ToString(" #0.00000;-#0.00000"));

            // Variance
            Console.WriteLine(@"{0} - Variance", fisherSnedecor.Variance.ToString(" #0.00000;-#0.00000"));

            // Standard deviation
            Console.WriteLine(@"{0} - Standard deviation", fisherSnedecor.StdDev.ToString(" #0.00000;-#0.00000"));

            // Skewness
            Console.WriteLine(@"{0} - Skewness", fisherSnedecor.Skewness.ToString(" #0.00000;-#0.00000"));
            Console.WriteLine();

            // 3. Generate 10 samples of the FisherSnedecor distribution
            Console.WriteLine(@"3. Generate 10 samples of the FisherSnedecor distribution");
            for (var i = 0; i < 10; i++)
            {
                Console.Write(fisherSnedecor.Sample().ToString("N05") + @" ");
            }

            Console.WriteLine();
            Console.WriteLine();

            // 4. Generate 100000 samples of the FisherSnedecor(50, 20) distribution and display histogram
            Console.WriteLine(@"4. Generate 100000 samples of the FisherSnedecor(50, 20) distribution and display histogram");
            var data = new double[100000];
            FisherSnedecor.Samples(data, 50, 20);
            ConsoleHelper.DisplayHistogram(data);
            Console.WriteLine();

            // 5. Generate 100000 samples of the FisherSnedecor(20, 10) distribution and display histogram
            Console.WriteLine(@"5. Generate 100000 samples of the FisherSnedecor(20, 10) distribution and display histogram");
            FisherSnedecor.Samples(data, 20, 10);
            ConsoleHelper.DisplayHistogram(data);
            Console.WriteLine();

            // 6. Generate 100000 samples of the FisherSnedecor(100, 100) distribution and display histogram
            Console.WriteLine(@"6. Generate 100000 samples of the FisherSnedecor(100, 100) distribution and display histogram");
            FisherSnedecor.Samples(data, 100, 100);
            ConsoleHelper.DisplayHistogram(data);
        }