public void BivariatePolynomialRegression()
{
// do a set of polynomial regression fits
// make sure not only that the fit parameters are what they should be, but that their variances/covariances are as claimed
Random rng = new Random(271828);
// define logistic parameters
double[] a = new double[] { 0.0, -1.0, 2.0, -3.0 };
// keep track of sample of returned a and b fit parameters
MultivariateSample A = new MultivariateSample(a.Length);
// also keep track of returned covariance estimates
// since these vary slightly from fit to fit, we will average them
SymmetricMatrix C = new SymmetricMatrix(a.Length);
// also keep track of test statistics
Sample F = new Sample();
// do 100 fits
for (int k = 0; k < 100; k++) {
// we should be able to draw x's from any distribution; noise should be drawn from a normal distribution
Distribution xd = new CauchyDistribution();
Distribution nd = new NormalDistribution(0.0, 4.0);
// generate a synthetic data set
BivariateSample s = new BivariateSample();
for (int j = 0; j < 20; j++) {
double x = xd.GetRandomValue(rng);
double y = nd.GetRandomValue(rng);
for (int i = 0; i < a.Length; i++) {
y += a[i] * MoreMath.Pow(x, i);
}
s.Add(x, y);
}
// do the regression
FitResult r = s.PolynomialRegression(a.Length - 1);
ColumnVector ps = r.Parameters;
//Console.WriteLine("{0} {1} {2}", ps[0], ps[1], ps[2]);
// record best fit parameters
A.Add(ps);
// record estimated covariances
C += r.CovarianceMatrix;
// record the fit statistic
F.Add(r.GoodnessOfFit.Statistic);
//Console.WriteLine("F={0}", r.GoodnessOfFit.Statistic);
}
C = (1.0 / A.Count) * C; // allow matrix division by real numbers
// check that mean parameter estimates are what they should be: the underlying population parameters
for (int i = 0; i < A.Dimension; i++) {
Console.WriteLine("{0} {1}", A.Column(i).PopulationMean, a[i]);
Assert.IsTrue(A.Column(i).PopulationMean.ConfidenceInterval(0.95).ClosedContains(a[i]));
}
// check that parameter covarainces are what they should be: the reported covariance estimates
for (int i = 0; i < A.Dimension; i++) {
for (int j = i; j < A.Dimension; j++) {
Console.WriteLine("{0} {1} {2} {3}", i, j, C[i, j], A.TwoColumns(i, j).PopulationCovariance);
Assert.IsTrue(A.TwoColumns(i, j).PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(C[i, j]));
}
}
// check that F is distributed as it should be
//Console.WriteLine(fs.KolmogorovSmirnovTest(new FisherDistribution(2, 48)).LeftProbability);
}
public void CauchyStudentAgreement()
{
StudentDistribution S = new StudentDistribution(1);
CauchyDistribution C = new CauchyDistribution();
// don't compare moments directly, because NaN != NaN
foreach (double P in probabilities) {
double xS = S.InverseLeftProbability(P);
double xC = C.InverseLeftProbability(P);
Console.WriteLine("{0} {1} {2}", P, xS, xC);
Assert.IsTrue(TestUtilities.IsNearlyEqual(xS, xC));
Assert.IsTrue(TestUtilities.IsNearlyEqual(S.ProbabilityDensity(xS), C.ProbabilityDensity(xC)));
}
}
public void SpearmanNullDistributionTest()
{
// pick independent distributions for x and y, which needn't be normal and needn't be related
Distribution xDistrubtion = new UniformDistribution();
Distribution yDistribution = new CauchyDistribution();
Random rng = new Random(1);
// generate bivariate samples of various sizes
foreach (int n in TestUtilities.GenerateIntegerValues(4, 64, 8)) {
Sample testStatistics = new Sample();
Distribution testDistribution = null;
for (int i = 0; i < 128; i++) {
BivariateSample sample = new BivariateSample();
for (int j = 0; j < n; j++) {
sample.Add(xDistrubtion.GetRandomValue(rng), yDistribution.GetRandomValue(rng));
}
TestResult result = sample.SpearmanRhoTest();
testStatistics.Add(result.Statistic);
testDistribution = result.Distribution;
}
TestResult r2 = testStatistics.KuiperTest(testDistribution);
Console.WriteLine("n={0} P={1}", n, r2.LeftProbability);
Assert.IsTrue(r2.RightProbability > 0.05);
Assert.IsTrue(testStatistics.PopulationMean.ConfidenceInterval(0.99).ClosedContains(testDistribution.Mean));
Assert.IsTrue(testStatistics.PopulationVariance.ConfidenceInterval(0.99).ClosedContains(testDistribution.Variance));
}
}
public void CauchyFWHM()
{
// Check that FWHM really is the full-width at half-maximum.
CauchyDistribution D = new CauchyDistribution(1.0, 2.0);
double p = D.ProbabilityDensity(D.Median);
Assert.IsTrue(TestUtilities.IsNearlyEqual(D.ProbabilityDensity(D.Median - D.FullWithAtHalfMaximum / 2.0), p / 2.0));
Assert.IsTrue(TestUtilities.IsNearlyEqual(D.ProbabilityDensity(D.Median + D.FullWithAtHalfMaximum / 2.0), p / 2.0));
}
public void TimeCauchyGenerators()
{
Random rng = new Random(1);
IDeviateGenerator nRng = new CauchyGenerator();
Distribution d = new CauchyDistribution();
Sample sample = new Sample();
Stopwatch timer = Stopwatch.StartNew();
double sum = 0.0;
for (int i = 0; i < 10000000; i++) {
sum += nRng.GetNext(rng);
//sum += d.InverseLeftProbability(rng.NextDouble());
//sample.Add(nRng.GetNext(rng));
}
timer.Stop();
//Console.WriteLine(sample.KolmogorovSmirnovTest(d).RightProbability);
Console.WriteLine(sum);
Console.WriteLine(timer.ElapsedMilliseconds);
}