public void MedianTest()
{
double[] samples = { 1, 5, 2, 5, 1, 7, 1, 9 };
EmpiricalDistribution target = new EmpiricalDistribution(samples);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
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 double[,] PFE(Product[] portfolioIn, Date valueDate, Date[] fwdValueDates, double[] percentiles)
{
CalculateAll(portfolioIn, valueDate, fwdValueDates);
double[,] pfe = new double[fwdValueDates.Length, percentiles.Length];
for (int col = 0; col < regressedValues.GetLength(1); col++)
{
EmpiricalDistribution xDist = new EmpiricalDistribution(regressedValues.GetColumn(col));
for (int percCount = 0; percCount < percentiles.Length; percCount++)
{
pfe[col, percCount] = xDist.InverseDistributionFunction(percentiles[percCount]);
}
}
return(pfe);
}
/// <summary>
/// Fits the cashflows to intrinsic functions of x. i.e. (x-K)^+ and (K-x)^+
/// </summary>
/// <returns></returns>
private double[][] GetIntrinsic(Date date, int order)
{
var col = _dates.FindIndex(d => d == date);
var result = new double[_regressors.GetLength(0)][];
for (var regressorNumber = 0; regressorNumber < _regressors.GetLength(2); regressorNumber++)
{
// For each regressor get the partition of the possible values
var xVec = GetSingleX(col, regressorNumber);
var xDist = new EmpiricalDistribution(xVec);
var strikes = new double[order - 1];
for (var i = 1; i < order; i++)
{
strikes[i - 1] = xDist.InverseDistributionFunction((double)i / order);
}
// Create the values of the basis functions for each regressor
for (var row = 0; row < _regressors.GetLength(0); row++)
{
double[] rowValues;
if (regressorNumber == 0
) // On the first pass for the first regressor, create the rows on the result matrix.
{
rowValues = new double[1 + order * _regressors.GetLength(2)];
rowValues[0] = 1;
result[row] = rowValues;
}
else
{
rowValues = result[row];
}
var x = _regressors[row, col, regressorNumber];
rowValues[1 + regressorNumber * order] = Math.Max(0, strikes[0] - x);
for (var orderCounter = 0; orderCounter < order - 1; orderCounter++)
{
rowValues[2 + regressorNumber * order + orderCounter] = Math.Max(0, x - strikes[orderCounter]);
}
}
}
return(result);
}