DistributionFunction() public method

Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
The Cumulative Distribution Function (CDF) describes the cumulative probability that a given value or any value smaller than it will occur.
public DistributionFunction ( double x ) : double
x double A single point in the distribution range.
return double
GeneralizedParetoDistribution Class Documentation
Esempio n. 1
0
        public void ConstructorTest()
        {
            #region doc_example1
            // Create a new Generalized Pareto Distribution with mu = 0, sigma = 0.42, xi = 3
            var pareto = new GeneralizedParetoDistribution(location: 0, scale: 0.42, shape: 3);

            // Common measures
            double mean = pareto.Mean;     // -0.21
            double median = pareto.Median; //  0.98
            double var = pareto.Variance;  // -0.00882
            double mode = pareto.Mode;     //  0.19185185523755152

            // Cumulative distribution functions
            double cdf = pareto.DistributionFunction(x: 1.4); // 0.55035568697739079
            double ccdf = pareto.ComplementaryDistributionFunction(x: 1.4); // 0.44964431302260921
            double icdf = pareto.InverseDistributionFunction(p: cdf); // 1.3999999035548829

            // Probability density functions
            double pdf = pareto.ProbabilityDensityFunction(x: 1.4); // 0.097325608879352654
            double lpdf = pareto.LogProbabilityDensityFunction(x: 1.4); // -2.3296931293597707

            // Hazard (failure rate) functions
            double hf = pareto.HazardFunction(x: 1.4); // 0.21645021645021648
            double chf = pareto.CumulativeHazardFunction(x: 1.4); // 0.79929842426612341

            // String representation
            string str = pareto.ToString(CultureInfo.InvariantCulture); // Pareto(x; μ = 0, σ = 0.42, ξ = 3)
            #endregion

            Assert.AreEqual(-0.21, mean);
            Assert.AreEqual(0.98, median);
            Assert.AreEqual(-0.008819999999999998, var);
            Assert.AreEqual(0.19185185523755152, mode, 1e-10);
            Assert.AreEqual(0.79929842426612341, chf);
            Assert.AreEqual(0.55035568697739079, cdf);
            Assert.AreEqual(0.097325608879352654, pdf);
            Assert.AreEqual(-2.3296931293597707, lpdf);
            Assert.AreEqual(0.21645021645021648, hf);
            Assert.AreEqual(0.44964431302260921, ccdf);
            Assert.AreEqual(1.40, icdf, 1e-5);
            Assert.AreEqual("Pareto(x; μ = 0, σ = 0.42, ξ = 3)", str);

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

            Assert.AreEqual(0.023289267355975959, range1.Min, 1e-8);
            Assert.AreEqual(1119.8599999998519, range1.Max, 1e-8);
            Assert.AreEqual(0.0042854196206619614, range2.Min, 1e-8);
            Assert.AreEqual(139999.86000000086, range2.Max, 1e-8);
            Assert.AreEqual(0.0042854196206619493, range3.Min, 1e-8);
            Assert.AreEqual(139999.86000000086, range3.Max, 1e-8);
        }