DistributionFunction() public method

Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
public DistributionFunction ( double x ) : double
x double A single point in the distribution range.
return double
        public void ConstructorTest()
        {
            var gompertz = new GompertzDistribution(eta: 4.2, b: 1.1);

            double median = gompertz.Median; // 0.13886469671401389

            double cdf = gompertz.DistributionFunction(x: 0.27); // 0.76599768199799145
            double pdf = gompertz.ProbabilityDensityFunction(x: 0.27); // 1.4549484164912097
            double lpdf = gompertz.LogProbabilityDensityFunction(x: 0.27); // 0.37497044741163688

            double ccdf = gompertz.ComplementaryDistributionFunction(x: 0.27); // 0.23400231800200855
            double icdf = gompertz.InverseDistributionFunction(p: cdf); // 0.26999999999766749

            double hf = gompertz.HazardFunction(x: 0.27); // 6.2176666834502088
            double chf = gompertz.CumulativeHazardFunction(x: 0.27); // 1.4524242576820101

            string str = gompertz.ToString(System.Globalization.CultureInfo.InvariantCulture);
              // "Gompertz(x; η = 4.2, b = 1.1)"

            Assert.AreEqual(0.13886469671401389, median);
            Assert.AreEqual(1.4524242576820101, chf);
            Assert.AreEqual(0.76599768199799145, cdf);
            Assert.AreEqual(1.4549484164912097, pdf);
            Assert.AreEqual(0.37497044741163688, lpdf);
            Assert.AreEqual(6.2176666834502088, hf);
            Assert.AreEqual(0.23400231800200855, ccdf);
            Assert.AreEqual(0.26999999999766749, icdf);
            Assert.AreEqual("Gompertz(x; η = 4.2, b = 1.1)", str);
        }
        public void ConstructorTest()
        {
            var gompertz = new GompertzDistribution(eta: 4.2, b: 1.1);

            try { double mean = gompertz.Mean; Assert.Fail(); }
            catch { }
            double median = gompertz.Median; // 0.13886469671401389
            double mode = gompertz.Mode;     // 0.0

            double cdf = gompertz.DistributionFunction(x: 0.27); // 0.76599768199799145
            double pdf = gompertz.ProbabilityDensityFunction(x: 0.27); // 1.4549484164912097
            double lpdf = gompertz.LogProbabilityDensityFunction(x: 0.27); // 0.37497044741163688

            double ccdf = gompertz.ComplementaryDistributionFunction(x: 0.27); // 0.23400231800200855
            double icdf = gompertz.InverseDistributionFunction(p: cdf); // 0.26999999999766749

            double hf = gompertz.HazardFunction(x: 0.27); // 6.2176666834502088
            double chf = gompertz.CumulativeHazardFunction(x: 0.27); // 1.4524242576820101

            string str = gompertz.ToString(System.Globalization.CultureInfo.InvariantCulture);
            // "Gompertz(x; η = 4.2, b = 1.1)"

            Assert.AreEqual(0.13886469671401389, median);
            Assert.AreEqual(0.0, mode);
            Assert.AreEqual(1.4524242576820101, chf);
            Assert.AreEqual(0.76599768199799145, cdf);
            Assert.AreEqual(1.4549484164912097, pdf);
            Assert.AreEqual(0.37497044741163688, lpdf);
            Assert.AreEqual(6.2176666834502088, hf);
            Assert.AreEqual(0.23400231800200855, ccdf);
            Assert.AreEqual(0.26999999999766749, icdf);
            Assert.AreEqual("Gompertz(x; η = 4.2, b = 1.1)", str);

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

            Assert.AreEqual(0.011035174219697141, range1.Min, 1e-6);
            Assert.AreEqual(0.48945776418276288, range1.Max, 1e-6);
            Assert.AreEqual(0.002172798720176344, range2.Min, 1e-6);
            Assert.AreEqual(0.67295877422837591, range2.Max, 1e-6);
            Assert.AreEqual(0.0021727987201762976, range3.Min, 1e-6);
            Assert.AreEqual(0.67295877422837591, range3.Max, 1e-6);
        }
        public void ConstructorTest2()
        {
            var gompertz = new GompertzDistribution(eta: 0.2, b: 1.1);

            try { double mean = gompertz.Mean; Assert.Fail(); }
            catch { }
            double median = gompertz.Median; // 1.3603945605494754
            double mode = gompertz.Mode;     // 1.4631253749400912

            double cdf = gompertz.DistributionFunction(x: 0.27); // 0.066825495660013834
            double pdf = gompertz.ProbabilityDensityFunction(x: 0.27); // 0.27629371549904269
            double lpdf = gompertz.LogProbabilityDensityFunction(x: 0.27); // -1.2862907925193949

            double ccdf = gompertz.ComplementaryDistributionFunction(x: 0.27); // 0.93317450433998617
            double icdf = gompertz.InverseDistributionFunction(p: cdf); // 0.27000016175969527

            double hf = gompertz.HazardFunction(x: 0.27); // 0.29607936587858147
            double chf = gompertz.CumulativeHazardFunction(x: 0.27); // 0.069163059889619516

            string str = gompertz.ToString(System.Globalization.CultureInfo.InvariantCulture);
            // "Gompertz(x; η = 4.2, b = 1.1)"

            Assert.AreEqual(1.3603945605494754, median);
            Assert.AreEqual(1.4631253749400912, mode);
            Assert.AreEqual(0.069163059889619516, chf);
            Assert.AreEqual(0.066825495660013834, cdf);
            Assert.AreEqual(0.27629371549904269, pdf);
            Assert.AreEqual(-1.2862907925193949, lpdf);
            Assert.AreEqual(0.29607936587858147, hf);
            Assert.AreEqual(0.93317450433998617, ccdf);
            Assert.AreEqual(0.27000016175969527, icdf);
            Assert.AreEqual("Gompertz(x; η = 0.2, b = 1.1)", str);
        }
        public void ConstructorTest13()
        {
            var original = new GompertzDistribution(eta: 4.2, b: 1.1);

            var gompertz = GeneralContinuousDistribution.FromDistributionFunction(
                original.Support, original.DistributionFunction);

            for (double i = -10; i < +10; i += 0.1)
            {
                double expected = original.DistributionFunction(i);
                double actual = gompertz.DistributionFunction(i);

                Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-7));
                Assert.IsFalse(double.IsNaN(expected));
                Assert.IsFalse(double.IsNaN(actual));
            }

            testGompertz(gompertz);
        }
        public void ConstructorTest12()
        {
            var original = new GompertzDistribution(eta: 4.2, b: 1.1);

            var gompertz = GeneralContinuousDistribution.FromDensityFunction(
                original.Support, original.ProbabilityDensityFunction);

            for (double i = -10; i < +7; i += 0.1)
            {
                double expected = original.DistributionFunction(i);
                double actual = gompertz.DistributionFunction(i);

                double diff = Math.Abs(expected - actual);
                Assert.AreEqual(expected, actual, 1e-3);
                Assert.IsFalse(double.IsNaN(expected));
                Assert.IsFalse(double.IsNaN(actual));
            }

            testGompertz(gompertz);
        }