Accord.Statistics.Distributions.Univariate.LevyDistribution.ProbabilityDensityFunction C# (CSharp) Method

        public override double ProbabilityDensityFunction(double x)
        {
            if (x < location)
                return 0;

            double z = x - location;
            double a = Math.Sqrt(scale / (2.0 * Math.PI));
            double b = Math.Exp(-(scale / (2 * z)));
            double c = Math.Pow(z, 3.0 / 2.0);

            return a * b / c;
        }

        public void ConstructorTest()
        {
            var levy = new LevyDistribution(location: 1, scale: 4.2);

            double mean = levy.Mean;     // +inf
            double median = levy.Median; // 10.232059220934481
            double mode = levy.Mode;     // NaN
            double var = levy.Variance;  // +inf

            double cdf = levy.DistributionFunction(x: 1.4); // 0.0011937454448720029
            double pdf = levy.ProbabilityDensityFunction(x: 1.4); // 0.016958939623898304
            double lpdf = levy.LogProbabilityDensityFunction(x: 1.4); // -4.0769601727487803

            double ccdf = levy.ComplementaryDistributionFunction(x: 1.4); // 0.99880625455512795
            double icdf = levy.InverseDistributionFunction(p: cdf); // 1.3999999

            double hf = levy.HazardFunction(x: 1.4); // 0.016979208476674869
            double chf = levy.CumulativeHazardFunction(x: 1.4); // 0.0011944585265140923

            string str = levy.ToString(CultureInfo.InvariantCulture); // Lévy(x; μ = 1, c = 4.2)

            // Tested against GNU R's rmutils package
            //
            // dlevy(1.4, m=1, s=4.2)
            // [1] 0.016958939623898303811
            //
            // plevy(1.4, m=1, s=4.2)
            // [1] 0.0011937454448720519196


            Assert.AreEqual(Double.PositiveInfinity, mean);
            Assert.AreEqual(10.232059220934481, median);
            Assert.IsTrue(Double.IsNaN(mode));
            Assert.AreEqual(Double.PositiveInfinity, var);
            Assert.AreEqual(0.0011944585265140923, chf);
            Assert.AreEqual(0.0011937454448720519196, cdf, 1e-10); // R
            Assert.AreEqual(0.016958939623898303811, pdf, 1e-10); // R
            Assert.AreEqual(-4.0769601727487803, lpdf);
            Assert.AreEqual(0.016979208476674869, hf);
            Assert.AreEqual(0.99880625455512795, ccdf);
            Assert.AreEqual(1.4, icdf, 1e-6);
            Assert.AreEqual("Lévy(x; μ = 1, c = 4.2)", str);

            double p = levy.DistributionFunction(levy.Median);
            Assert.AreEqual(0.5, p, 1e-10);
            Assert.IsFalse(Double.IsNaN(p));

            var range1 = levy.GetRange(0.95);
            var range2 = levy.GetRange(0.99);
            var range3 = levy.GetRange(0.01);

            Assert.AreEqual(2.0933346408334241, range1.Min);
            Assert.AreEqual(1069.1206671123464, range1.Max);
            Assert.AreEqual(1.6330166470647871, range2.Min);
            Assert.AreEqual(26737.630417446126, range2.Max);
            Assert.AreEqual(1.6330166470647871, range3.Min);
            Assert.AreEqual(26737.630417446126, range3.Max);
        }