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 mode = distribution.Mode; // 3
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, mode);
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, 1e-15);
Assert.AreEqual(-1.7067405350495708, lpdf);
Assert.AreEqual(1.6331065212852196, hf, 1e-15);
Assert.AreEqual(0.11111111111111116, ccdf);
Assert.AreEqual(4.1999999999999993, icdf);
Assert.AreEqual("Fn(x; S)", str);
var range1 = distribution.GetRange(0.95);
var range2 = distribution.GetRange(0.99);
var range3 = distribution.GetRange(0.01);
Assert.AreEqual(0.99999947547912593, range1.Min);
Assert.AreEqual(5.0000002464240794, range1.Max);
Assert.AreEqual(0.99999913215637204, range2.Min);
Assert.AreEqual(5.0000004605903117, range2.Max);
Assert.AreEqual(0.99999913215637204, range3.Min);
Assert.AreEqual(5.0000004605903117, range3.Max);
}
public void LogProbabilityDensityFunctionTest()
{
double[] samples = { 1, 5, 2, 5, 1, 7, 1, 9, 4, 2 };
EmpiricalDistribution target = new EmpiricalDistribution(samples, 1);
Assert.AreEqual(1.0, target.Smoothing);
double actual;
double expected;
actual = target.LogProbabilityDensityFunction(1);
expected = System.Math.Log(0.16854678051819402);
Assert.AreEqual(expected, actual, 1e-6);
actual = target.LogProbabilityDensityFunction(2);
expected = System.Math.Log(0.15866528844260089);
Assert.AreEqual(expected, actual, 1e-6);
actual = target.LogProbabilityDensityFunction(3);
expected = System.Math.Log(0.0996000842425018);
Assert.AreEqual(expected, actual, 1e-6);
actual = target.LogProbabilityDensityFunction(4);
expected = System.Math.Log(0.1008594542833362);
Assert.AreEqual(expected, actual, 1e-6);
actual = target.LogProbabilityDensityFunction(6);
expected = System.Math.Log(0.078460710909263);
Assert.AreEqual(expected, actual, 1e-6);
actual = target.LogProbabilityDensityFunction(8);
expected = System.Math.Log(0.049293898826709738);
Assert.AreEqual(expected, actual, 1e-6);
}
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);
Assert.AreEqual(-1.8609305013898356, lpdf);
Assert.AreEqual(1.3997505972727771, hf);
Assert.AreEqual(0.11111111111111116, ccdf);
Assert.AreEqual(4.1999999999999993, icdf);
Assert.AreEqual("Fn(x; S)", str);
}
public void WeightedEmpiricalDistributionConstructorTest2()
{
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);
double[] 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 };
weights = weights.Divide(weights.Sum());
var target = new EmpiricalDistribution(samples, weights, distribution.Smoothing);
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(1.1685534824642432, target.StandardDeviation);
Assert.AreEqual(distribution.Support.Min, target.Support.Min);
Assert.AreEqual(distribution.Support.Max, target.Support.Max);
Assert.AreEqual(1.3655172413793104, target.Variance);
Assert.AreEqual(target.Weights, weights);
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, 1e-15);
expected = distribution.CumulativeHazardFunction(x);
actual = target.CumulativeHazardFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
expected = distribution.DistributionFunction(x);
actual = target.DistributionFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
expected = distribution.HazardFunction(x);
actual = target.HazardFunction(x);
Assert.AreEqual(expected, actual, 1e-14);
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, 1e-14);
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);
}
}