public void BivariateNonlinearFitSimple()
{
double t0 = 3.0;
double s0 = 1.0;
ContinuousDistribution xDistribution = new CauchyDistribution(0.0, 2.0);
ContinuousDistribution eDistribution = new NormalDistribution(0.0, 0.5);
Random rng = new Random(5);
List <double> x = TestUtilities.CreateDataSample(rng, xDistribution, 48).ToList();
List <double> y = x.Select(z => Math.Sin(2.0 * Math.PI * z / t0 + s0) + eDistribution.GetRandomValue(rng)).ToList();
Func <IReadOnlyDictionary <string, double>, double, double> fitFunction = (d, z) => {
double t = d["Period"];
double s = d["Phase"];
return(Math.Sin(2.0 * Math.PI * z / t + s));
};
Dictionary <string, double> start = new Dictionary <string, double>()
{
{ "Period", 2.5 }, { "Phase", 1.5 }
};
NonlinearRegressionResult result = y.NonlinearRegression(x, fitFunction, start);
Assert.IsTrue(result.Parameters["Period"].Estimate.ConfidenceInterval(0.99).ClosedContains(t0));
Assert.IsTrue(result.Parameters["Phase"].Estimate.ConfidenceInterval(0.99).ClosedContains(s0));
for (int i = 0; i < x.Count; i++)
{
double yp = result.Predict(x[i]);
Assert.IsTrue(TestUtilities.IsNearlyEqual(result.Residuals[i], y[i] - yp));
}
}
public void BivariatePolynomialRegressionSimple()
{
// Pick a simple polynomial
Polynomial p = Polynomial.FromCoefficients(3.0, -2.0, 1.0);
// Use it to generate a data set
Random rng = new Random(1);
ContinuousDistribution xDistribution = new CauchyDistribution(1.0, 2.0);
ContinuousDistribution errorDistribution = new NormalDistribution(0.0, 3.0);
List <double> xs = new List <double>(TestUtilities.CreateDataSample(rng, xDistribution, 10));
List <double> ys = new List <double>(xs.Select(x => p.Evaluate(x) + errorDistribution.GetRandomValue(rng)));
PolynomialRegressionResult fit = Bivariate.PolynomialRegression(ys, xs, p.Degree);
// Parameters should agree
Assert.IsTrue(fit.Parameters.Count == p.Degree + 1);
for (int k = 0; k <= p.Degree; k++)
{
Assert.IsTrue(fit.Coefficient(k).ConfidenceInterval(0.99).ClosedContains(p.Coefficient(k)));
}
// Residuals should agree
Assert.IsTrue(fit.Residuals.Count == xs.Count);
for (int i = 0; i < xs.Count; i++)
{
double z = ys[i] - fit.Predict(xs[i]).Value;
Assert.IsTrue(TestUtilities.IsNearlyEqual(z, fit.Residuals[i]));
}
// Intercept is same as coefficient of x^0
Assert.IsTrue(fit.Intercept == fit.Coefficient(0));
}
public void StreamSampleSummaryAgreement()
{
// Streaming properties should give same answers as list methods.
Random rng = new Random(2);
List <double> sample = new List <double>(TestUtilities.CreateDataSample(rng, new UniformDistribution(Interval.FromEndpoints(-4.0, 3.0)), 32));
SummaryStatistics summary = new SummaryStatistics(sample);
Assert.IsTrue(summary.Count == sample.Count);
Assert.IsTrue(TestUtilities.IsNearlyEqual(sample.Mean(), summary.Mean));
Assert.IsTrue(TestUtilities.IsNearlyEqual(sample.Variance(), summary.Variance));
Assert.IsTrue(TestUtilities.IsNearlyEqual(sample.PopulationMean(), summary.PopulationMean));
Assert.IsTrue(TestUtilities.IsNearlyEqual(sample.PopulationVariance(), summary.PopulationVariance));
Assert.IsTrue(sample.Minimum() == summary.Minimum);
Assert.IsTrue(sample.Maximum() == summary.Maximum);
}
public void StreamingSampleSummaryCombination()
{
// Combining partial summaries should give same answer as full summary
Random rng = new Random(1);
List <double> sample = new List <double>(TestUtilities.CreateDataSample(rng, new UniformDistribution(Interval.FromEndpoints(-4.0, 3.0)), 64));
SummaryStatistics summary = new SummaryStatistics(sample);
Assert.IsTrue(summary.Count == sample.Count);
for (int i = 0; i < 4; i++)
{
// Pick a split point in the data
int m = rng.Next(0, sample.Count);
// Create a summary of the first part.
SummaryStatistics summary1 = new SummaryStatistics(sample.Take(m));
Assert.IsTrue(summary1.Count == m);
// Create a summary of the second part.
SummaryStatistics summary2 = new SummaryStatistics(sample.Skip(m));
Assert.IsTrue(summary2.Count == sample.Count - m);
// Combine them. Their summary statistics should agree with the original summary.
SummaryStatistics combined = SummaryStatistics.Combine(summary1, summary2);
Assert.IsTrue(combined.Count == summary.Count);
Assert.IsTrue(TestUtilities.IsNearlyEqual(combined.Mean, summary.Mean));
Assert.IsTrue(TestUtilities.IsNearlyEqual(combined.Variance, summary.Variance));
Assert.IsTrue(TestUtilities.IsNearlyEqual(combined.StandardDeviation, summary.StandardDeviation));
Assert.IsTrue(TestUtilities.IsNearlyEqual(combined.Skewness, summary.Skewness));
Assert.IsTrue(TestUtilities.IsNearlyEqual(combined.PopulationMean, summary.PopulationMean));
Assert.IsTrue(TestUtilities.IsNearlyEqual(combined.PopulationVariance, summary.PopulationVariance));
Assert.IsTrue(combined.Minimum == summary.Minimum);
Assert.IsTrue(combined.Maximum == summary.Maximum);
}
}
public void TwoSampleKolmogorovNullDistributionTest()
{
Random rng = new Random(4);
ContinuousDistribution population = new ExponentialDistribution();
int[] sizes = new int[] { 23, 30, 175 };
foreach (int na in sizes)
{
foreach (int nb in sizes)
{
Sample d = new Sample();
ContinuousDistribution nullDistribution = null;
for (int i = 0; i < 128; i++)
{
List <double> a = TestUtilities.CreateDataSample(rng, population, na).ToList();
List <double> b = TestUtilities.CreateDataSample(rng, population, nb).ToList();
TestResult r = Univariate.KolmogorovSmirnovTest(a, b);
d.Add(r.Statistic.Value);
nullDistribution = r.Statistic.Distribution;
}
// Only do full KS test if the number of bins is larger than the sample size, otherwise we are going to fail
// because the KS test detects the granularity of the distribution.
TestResult mr = d.KolmogorovSmirnovTest(nullDistribution);
if (AdvancedIntegerMath.LCM(na, nb) > d.Count)
{
Assert.IsTrue(mr.Probability > 0.01);
}
// But always test that mean and standard deviation are as expected
Assert.IsTrue(d.PopulationMean.ConfidenceInterval(0.99).ClosedContains(nullDistribution.Mean));
Assert.IsTrue(d.PopulationStandardDeviation.ConfidenceInterval(0.99).ClosedContains(nullDistribution.StandardDeviation));
// This test is actually a bit sensitive, probably because the discrete-ness of the underlying distribution
// and the inaccuracy of the asymptotic approximation for intermediate sample size make strict comparisons iffy.
}
}
}