public void EmpiricalDistributionConstructorTest5() { double[] samples = { 5, 5, 1, 4, 1, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 3 }; EmpiricalDistribution distribution = new EmpiricalDistribution(samples, FaultySmoothingRule(samples)); double mean = distribution.Mean; // 3 double median = distribution.Median; // 2.9999993064186787 double var = distribution.Variance; // 1.2941176470588236 double chf = distribution.CumulativeHazardFunction(x: 4.2); // 2.1972245773362191 double cdf = distribution.DistributionFunction(x: 4.2); // 0.88888888888888884 double pdf = distribution.ProbabilityDensityFunction(x: 4.2); // 0.15552784414141974 double lpdf = distribution.LogProbabilityDensityFunction(x: 4.2); // -1.8609305013898356 double hf = distribution.HazardFunction(x: 4.2); // 1.3997505972727771 double ccdf = distribution.ComplementaryDistributionFunction(x: 4.2); //0.11111111111111116 double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.1999999999999993 double smoothing = distribution.Smoothing; // 1.9144923416414432 string str = distribution.ToString(); // Fn(x; S) Assert.AreEqual(samples, distribution.Samples); Assert.AreEqual(1.9144923416414432, smoothing, 1.0e-15); Assert.AreEqual(3.0, mean); Assert.AreEqual(2.9999993064186787, median); Assert.AreEqual(1.2941176470588236, var); Assert.AreEqual(2.1972245773362191, chf); Assert.AreEqual(0.88888888888888884, cdf); Assert.AreEqual(0.15552784414141974, pdf, 1e-15); Assert.AreEqual(-1.8609305013898356, lpdf); Assert.AreEqual(1.3997505972727771, hf, 1e-15); Assert.AreEqual(0.11111111111111116, ccdf); Assert.AreEqual(4.1999999999999993, icdf); Assert.AreEqual("Fn(x; S)", str); }
public void EmpiricalDistributionConstructorTest3() { double[] samples = { 5, 5, 1, 4, 1, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 3 }; EmpiricalDistribution distribution = new EmpiricalDistribution(samples); double mean = distribution.Mean; // 3 double median = distribution.Median; // 2.9999993064186787 double var = distribution.Variance; // 1.2941176470588236 double chf = distribution.CumulativeHazardFunction(x: 4.2); // 2.1972245773362191 double cdf = distribution.DistributionFunction(x: 4.2); // 0.88888888888888884 double pdf = distribution.ProbabilityDensityFunction(x: 4.2); // 0.181456280142802 double lpdf = distribution.LogProbabilityDensityFunction(x: 4.2); // -1.7067405350495708 double hf = distribution.HazardFunction(x: 4.2); // 1.6331065212852196 double ccdf = distribution.ComplementaryDistributionFunction(x: 4.2); //0.11111111111111116 double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.1999999999999993 double smoothing = distribution.Smoothing; // 0.67595864392399474 string str = distribution.ToString(); // Fn(x; S) Assert.AreEqual(samples, distribution.Samples); Assert.AreEqual(0.67595864392399474, smoothing); Assert.AreEqual(3.0, mean); Assert.AreEqual(2.9999993064186787, median); Assert.AreEqual(1.2941176470588236, var); Assert.AreEqual(2.1972245773362191, chf); Assert.AreEqual(0.88888888888888884, cdf); Assert.AreEqual(0.18145628014280227, pdf); Assert.AreEqual(-1.7067405350495708, lpdf); Assert.AreEqual(1.6331065212852196, hf); Assert.AreEqual(0.11111111111111116, ccdf); Assert.AreEqual(4.1999999999999993, icdf); Assert.AreEqual("Fn(x; S)", str); }
public void WeightedEmpiricalDistributionConstructorTest() { double[] original = { 5, 5, 1, 4, 1, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 3 }; var distribution = new EmpiricalDistribution(original); int[] weights = { 2, 1, 1, 1, 2, 3, 1, 3, 1, 1, 1, 1 }; double[] samples = { 5, 1, 4, 1, 2, 3, 4, 3, 4, 3, 2, 3 }; var target = new EmpiricalDistribution(samples, weights); Assert.AreEqual(distribution.Entropy, target.Entropy, 1e-10); Assert.AreEqual(distribution.Mean, target.Mean); Assert.AreEqual(distribution.Median, target.Median); Assert.AreEqual(distribution.Mode, target.Mode); Assert.AreEqual(distribution.Quartiles.Min, target.Quartiles.Min); Assert.AreEqual(distribution.Quartiles.Max, target.Quartiles.Max); Assert.AreEqual(distribution.Smoothing, target.Smoothing); Assert.AreEqual(distribution.StandardDeviation, target.StandardDeviation); Assert.AreEqual(distribution.Support.Min, target.Support.Min); Assert.AreEqual(distribution.Support.Max, target.Support.Max); Assert.AreEqual(distribution.Variance, target.Variance); Assert.IsTrue(target.Weights.IsEqual(weights.Divide(weights.Sum()))); Assert.AreEqual(target.Samples, samples); for (double x = 0; x < 6; x += 0.1) { double actual, expected; expected = distribution.ComplementaryDistributionFunction(x); actual = target.ComplementaryDistributionFunction(x); Assert.AreEqual(expected, actual); expected = distribution.CumulativeHazardFunction(x); actual = target.CumulativeHazardFunction(x); Assert.AreEqual(expected, actual); expected = distribution.DistributionFunction(x); actual = target.DistributionFunction(x); Assert.AreEqual(expected, actual); expected = distribution.HazardFunction(x); actual = target.HazardFunction(x); Assert.AreEqual(expected, actual, 1e-15); expected = distribution.InverseDistributionFunction(Accord.Math.Tools.Scale(0, 6, 0, 1, x)); actual = target.InverseDistributionFunction(Accord.Math.Tools.Scale(0, 6, 0, 1, x)); Assert.AreEqual(expected, actual); expected = distribution.LogProbabilityDensityFunction(x); actual = target.LogProbabilityDensityFunction(x); Assert.AreEqual(expected, actual, 1e-15); expected = distribution.ProbabilityDensityFunction(x); actual = target.ProbabilityDensityFunction(x); Assert.AreEqual(expected, actual, 1e-15); expected = distribution.QuantileDensityFunction(Accord.Math.Tools.Scale(0, 6, 0, 1, x)); actual = target.QuantileDensityFunction(Accord.Math.Tools.Scale(0, 6, 0, 1, x)); Assert.AreEqual(expected, actual, 1e-10); } }
public void DistributionFunctionTest() { double[] samples = { 1, 5, 2, 5, 1, 7, 1, 9 }; EmpiricalDistribution target = new EmpiricalDistribution(samples); Assert.AreEqual(0.000, target.DistributionFunction(0)); Assert.AreEqual(0.375, target.DistributionFunction(1)); Assert.AreEqual(0.500, target.DistributionFunction(2)); Assert.AreEqual(0.750, target.DistributionFunction(5)); Assert.AreEqual(0.875, target.DistributionFunction(7)); Assert.AreEqual(1.000, target.DistributionFunction(9)); }
private List <RecordMongo> typicalDay(List <List <RecordMongo> > possDayValues, string vcode) { List <double> longTermValues = new List <double>(); //list of all candidate days cdfs List <EmpiricalDistribution> dayCDFS = new List <EmpiricalDistribution>(); foreach (List <RecordMongo> day in possDayValues) { List <double> dayValues = new List <double>(); foreach (RecordMongo rm in day) { if (rm.value != -999.9) { //only actual values in the cdfs longTermValues.Add(rm.value); dayValues.Add(rm.value); } } dayCDFS.Add(new EmpiricalDistribution(dayValues.ToArray())); } //longterm cdf all days found EmpiricalDistribution longterm = new EmpiricalDistribution(longTermValues.ToArray()); List <double> finkelSch = new List <double>(); var range = longterm.GetRange(0.9); double inc = (range.Max - range.Min) / 20; foreach (EmpiricalDistribution candDay in dayCDFS) { double sample = range.Min; double fs = 0; while (sample <= range.Max) { fs += Math.Abs(candDay.DistributionFunction(sample) - longterm.DistributionFunction(sample)); sample += inc; } //24 is the n values per day finkelSch.Add(fs / 24); } int minindex = finkelSch.IndexOf(finkelSch.Min()); List <RecordMongo> selectedday = possDayValues[minindex]; return(selectedday); }
/// <summary> /// Constructs a Chi-Square Test. /// </summary> /// public ChiSquareTest(double[] observations, IUnivariateDistribution hypothesizedDistribution) { int n = observations.Length; var E = new EmpiricalDistribution(observations); var F = hypothesizedDistribution; // Create bins with the observations int bins = (int)Math.Ceiling(1 + Math.Log(observations.Length)); double[] ebins = new double[bins + 1]; for (int i = 0; i <= bins; i++) { double p = i / (double)bins; ebins[i] = F.InverseDistributionFunction(p); } double[] expected = new double[bins - 1]; int size = expected.Length; for (int i = 0; i < expected.Length; i++) { double a = ebins[i]; double b = ebins[i + 1]; if (Double.IsPositiveInfinity(b)) { break; } double Fa = F.DistributionFunction(a); double Fb = F.DistributionFunction(b); double samples = Math.Abs(Fb - Fa) * n; expected[i] = samples; if (samples < 5) { size = i + 1; for (int j = i + 1; j < ebins.Length - 1; j++) { ebins[j] = ebins[j + 1]; } ebins[ebins.Length - 1] = Double.PositiveInfinity; i--; } } ebins = ebins.Submatrix(size + 2); expected = expected.Submatrix(ebins.Length - 2); double[] observed = new double[expected.Length]; for (int i = 0; i < observed.Length; i++) { double a = ebins[i]; double b = ebins[i + 1]; observed[i] = E.DistributionFunction(a, b) * n; } double sum = compute(expected, observed); Compute(sum, bins - 1); }