Accord.Statistics.Distributions.Univariate.TDistribution.DistributionFunction C# (CSharp) Method

        public override double DistributionFunction(double x)
        {
            double v = DegreesOfFreedom;
            double sqrt = Math.Sqrt(x * x + v);
            double u = (x + sqrt) / (2 * sqrt);
            return Beta.Incomplete(v / 2.0, v / 2.0, u);
        }

        public void ConstructorTest()
        {
            var t = new TDistribution(degreesOfFreedom: 4.2);

            double mean = t.Mean;     // 0.0
            double median = t.Median; // 0.0
            double var = t.Variance;  // 1.9090909090909089

            double cdf = t.DistributionFunction(x: 1.4); // 0.88456136730659074
            double pdf = t.ProbabilityDensityFunction(x: 1.4); // 0.13894002185341031
            double lpdf = t.LogProbabilityDensityFunction(x: 1.4); // -1.9737129364307417

            double ccdf = t.ComplementaryDistributionFunction(x: 1.4); // 0.11543863269340926
            double icdf = t.InverseDistributionFunction(p: cdf); // 1.4000000000000012

            double hf = t.HazardFunction(x: 1.4); // 1.2035833984833988
            double chf = t.CumulativeHazardFunction(x: 1.4); // 2.1590162088918525

            string str = t.ToString(CultureInfo.InvariantCulture); // T(x; df = 4.2)

            Assert.AreEqual(0.0, mean);
            Assert.AreEqual(0.0, median);
            Assert.AreEqual(1.9090909090909089, var);
            Assert.AreEqual(2.1590162088918525, chf);
            Assert.AreEqual(0.88456136730659074, cdf);
            Assert.AreEqual(0.13894002185341031, pdf);
            Assert.AreEqual(-1.9737129364307417, lpdf);
            Assert.AreEqual(1.2035833984833988, hf);
            Assert.AreEqual(0.11543863269340926, ccdf);
            Assert.AreEqual(1.4000000000000012, icdf);
            Assert.AreEqual("T(x; df = 4.2)", str);
        }