DistributionFunction() public méthode

Gets the cumulative distribution function (cdf) for this distribution evaluated at point k.
The Cumulative Distribution Function (CDF) describes the cumulative probability that a given value or any value smaller than it will occur.
public DistributionFunction ( double w ) : double
w double A single point in the distribution range.
Résultat double
WilcoxonDistribution Class Documentation
Exemple #1
0
        public void ConstructorTest()
        {
            double[] ranks = { 1, 2, 3, 4, 5.5, 5.5, 7, 8, 9, 10, 11, 12 };

            var W = new WilcoxonDistribution(ranks);

            double mean = W.Mean;     // 39.0
            double median = W.Median; // 38.5
            double var = W.Variance;  // 162.5

            double cdf = W.DistributionFunction(w: 42); // 0.60817384423279575
            double pdf = W.ProbabilityDensityFunction(w: 42); // 0.38418508862319295
            double lpdf = W.LogProbabilityDensityFunction(w: 42); // 0.38418508862319295

            double ccdf = W.ComplementaryDistributionFunction(x: 42); // 0.39182615576720425
            double icdf = W.InverseDistributionFunction(p: cdf); // 42
            double icdf2 = W.InverseDistributionFunction(p: 0.5); // 42

            double hf = W.HazardFunction(x: 42); // 0.98049883339449373
            double chf = W.CumulativeHazardFunction(x: 42); // 0.936937017743799

            string str = W.ToString(); // "W+(x; R)"

            Assert.AreEqual(39.0, mean);
            Assert.AreEqual(38.5, median, 1e-6);
            Assert.AreEqual(162.5, var);
            Assert.AreEqual(0.936937017743799, chf);
            Assert.AreEqual(0.60817384423279575, cdf);
            Assert.AreEqual(0.38418508862319295, pdf);
            Assert.AreEqual(-0.95663084089698047, lpdf);
            Assert.AreEqual(0.98049883339449373, hf);
            Assert.AreEqual(0.39182615576720425, ccdf);
            Assert.AreEqual(42, icdf, 1e-6);
            Assert.AreEqual("W+(x; R)", str);
        }
Exemple #2
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        public void ConstructorTest2()
        {
            double[] ranks = { 1, 2, 3, 4, 5.5, 5.5, 7, 8, 9, 10, 11, 12 };

            var W = new WilcoxonDistribution(ranks, forceExact: true);

            double mean = W.Mean;     // 39
            double median = W.Median; // 39
            double var = W.Variance;  // 162.5

            double cdf = W.DistributionFunction(w: 42); // 0.582763671875
            double pdf = W.ProbabilityDensityFunction(w: 42); // 0.014404296875
            double lpdf = W.LogProbabilityDensityFunction(w: 42); // -4.2402287228136233

            double ccdf = W.ComplementaryDistributionFunction(x: 42); // 0.417236328125
            double icdf = W.InverseDistributionFunction(p: cdf); // 41.965447500067114
            double icdf2 = W.InverseDistributionFunction(p: 0.5); // 39.000000487005138

            double hf = W.HazardFunction(x: 42); // 0.03452311293153891
            double chf = W.CumulativeHazardFunction(x: 42); // 0.87410248360375287

            string str = W.ToString(); // "W+(x; R)"

            Assert.AreEqual(39.0, mean);
            Assert.AreEqual(39.0, median, 1e-6);
            Assert.AreEqual(162.5, var);
            Assert.AreEqual(0.87410248360375287, chf);
            Assert.AreEqual(0.582763671875, cdf);
            Assert.AreEqual(0.014404296875, pdf);
            Assert.AreEqual(-4.2402287228136233, lpdf);
            Assert.AreEqual(0.03452311293153891, hf);
            Assert.AreEqual(0.417236328125, ccdf);
            Assert.AreEqual(42, icdf, 0.05);
            Assert.AreEqual("W+(x; R)", str);

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

            Assert.AreEqual(17.999999736111114, range1.Min);
            Assert.AreEqual(60.000000315408002, range1.Max);
            Assert.AreEqual(10.000000351098127, range2.Min);
            Assert.AreEqual(67.99999981945885, range2.Max);
            Assert.AreEqual(10.000000351098119, range3.Min);
            Assert.AreEqual(67.99999981945885, range3.Max);
        }
Exemple #3
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        public void CumulativeExactTest()
        {
            // example from https://onlinecourses.science.psu.edu/stat414/node/319

            double[] ranks = 
            {
                22, 2, 13, 24, 16, 15, 25, 10, 9, 11, 5, 
                17, 12, 20, 14, 30, 8, 6, 26, 19, 29, 27, 3, 28,
                7, 21, 23, 1, 18, 4
            };

            WilcoxonDistribution target = new WilcoxonDistribution(ranks);

            Assert.AreEqual(232.5, target.Mean);
            Assert.AreEqual(2363.75, target.Variance);
            Assert.AreEqual(Math.Sqrt(2363.75), target.StandardDeviation);

            double actual = target.DistributionFunction(200);
            double expected = 0.2546;
            Assert.AreEqual(expected, actual, 1e-2);

            double inv = target.InverseDistributionFunction(actual);

            Assert.AreEqual(200, inv);
        }
Exemple #4
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        public void CumulativeTest()
        {
            // Example from https://onlinecourses.science.psu.edu/stat414/node/319

            double[] ranks = { 1, 2, 3 };

            WilcoxonDistribution target = new WilcoxonDistribution(ranks);

            double[] probabilities = { 0.0, 1 / 8.0, 1 / 8.0, 1 / 8.0, 2 / 8.0, 1 / 8.0, 1 / 8.0, 1 / 8.0 };
            double[] expected = Accord.Math.Matrix.CumulativeSum(probabilities);

            for (int i = 0; i < expected.Length; i++)
            {
                // P(W<=i)
                double actual = target.DistributionFunction(i);
                Assert.AreEqual(expected[i], actual);
            }
        }