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);
}