public void WaldFit()
{
WaldDistribution wald = new WaldDistribution(3.5, 2.5);
FrameTable results = new FrameTable();
results.AddColumns <double>("Mean", "Shape", "MeanVariance", "ShapeVariance", "MeanShapeCovariance");
for (int i = 0; i < 128; i++)
{
Sample sample = SampleTest.CreateSample(wald, 16, i);
WaldFitResult result = WaldDistribution.FitToSample(sample);
Assert.IsTrue(result.Mean.Value == result.Parameters.ValuesVector[result.Parameters.IndexOf("Mean")]);
Assert.IsTrue(result.Shape.Value == result.Parameters.ValuesVector[result.Parameters.IndexOf("Shape")]);
Assert.IsTrue(TestUtilities.IsNearlyEqual(result.Parameters.VarianceOf("Mean"), MoreMath.Sqr(result.Mean.Uncertainty)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(result.Parameters.VarianceOf("Shape"), MoreMath.Sqr(result.Shape.Uncertainty)));
results.AddRow(
result.Mean.Value, result.Shape.Value,
result.Parameters.VarianceOf("Mean"), result.Parameters.VarianceOf("Shape"), result.Parameters.CovarianceOf("Mean", "Shape")
);
}
Assert.IsTrue(results["Mean"].As <double>().PopulationMean().ConfidenceInterval(0.99).ClosedContains(wald.Mean));
Assert.IsTrue(results["Shape"].As <double>().PopulationMean().ConfidenceInterval(0.99).ClosedContains(wald.Shape));
Assert.IsTrue(results["Mean"].As <double>().PopulationVariance().ConfidenceInterval(0.99).ClosedContains(results["MeanVariance"].As <double>().Median()));
Assert.IsTrue(results["Shape"].As <double>().PopulationVariance().ConfidenceInterval(0.99).ClosedContains(results["ShapeVariance"].As <double>().Median()));
Assert.IsTrue(results["Mean"].As <double>().PopulationCovariance(results["Shape"].As <double>()).ConfidenceInterval(0.99).ClosedContains(results["MeanShapeCovariance"].As <double>().Median()));
}
public void ExponentialFitUncertainty()
{
// check that the uncertainty in reported fit parameters is actually meaningful
// it should be the standard deviation of fit parameter values in a sample of many fits
// define a population distribution
ExponentialDistribution distribution = new ExponentialDistribution(4.0);
// draw a lot of samples from it; fit each sample and
// record the reported parameter value and error of each
Sample values = new Sample();
Sample uncertainties = new Sample();
for (int i = 0; i < 128; i++)
{
Sample sample = SampleTest.CreateSample(distribution, 8, i);
ExponentialFitResult fit = ExponentialDistribution.FitToSample(sample);
UncertainValue lambda = fit.Parameters[0].Estimate;
values.Add(lambda.Value);
uncertainties.Add(lambda.Uncertainty);
}
// the reported values should agree with the source distribution
Assert.IsTrue(values.PopulationMean.ConfidenceInterval(0.95).ClosedContains(distribution.Mean));
// the reported errors should agree with the standard deviation of the reported parameters
Assert.IsTrue(values.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(uncertainties.Mean));
}
public void GumbelFit()
{
GumbelDistribution d = new GumbelDistribution(-1.0, 2.0);
MultivariateSample parameters = new MultivariateSample(2);
MultivariateSample variances = new MultivariateSample(3);
// Do a bunch of fits, record reported parameters and variances
for (int i = 0; i < 32; i++)
{
Sample s = SampleTest.CreateSample(d, 64, i);
GumbelFitResult r = GumbelDistribution.FitToSample(s);
parameters.Add(r.Location.Value, r.Scale.Value);
variances.Add(r.Parameters.CovarianceMatrix[0, 0], r.Parameters.CovarianceMatrix[1, 1], r.Parameters.CovarianceMatrix[0, 1]);
Assert.IsTrue(r.GoodnessOfFit.Probability > 0.01);
}
// The reported parameters should agree with the underlying parameters
Assert.IsTrue(parameters.Column(0).PopulationMean.ConfidenceInterval(0.99).ClosedContains(d.Location));
Assert.IsTrue(parameters.Column(1).PopulationMean.ConfidenceInterval(0.99).ClosedContains(d.Scale));
// The reported covariances should agree with the observed covariances
Assert.IsTrue(parameters.Column(0).PopulationVariance.ConfidenceInterval(0.99).ClosedContains(variances.Column(0).Mean));
Assert.IsTrue(parameters.Column(1).PopulationVariance.ConfidenceInterval(0.99).ClosedContains(variances.Column(1).Mean));
Assert.IsTrue(parameters.TwoColumns(0, 1).PopulationCovariance.ConfidenceInterval(0.99).ClosedContains(variances.Column(2).Mean));
}
public void WaldFit()
{
WaldDistribution wald = new WaldDistribution(3.5, 2.5);
BivariateSample parameters = new BivariateSample();
MultivariateSample variances = new MultivariateSample(3);
for (int i = 0; i < 128; i++)
{
Sample s = SampleTest.CreateSample(wald, 16, i);
FitResult r = WaldDistribution.FitToSample(s);
parameters.Add(r.Parameters[0], r.Parameters[1]);
variances.Add(r.Covariance(0, 0), r.Covariance(1, 1), r.Covariance(0, 1));
Assert.IsTrue(r.GoodnessOfFit.Probability > 0.01);
}
Assert.IsTrue(parameters.X.PopulationMean.ConfidenceInterval(0.99).ClosedContains(wald.Mean));
Assert.IsTrue(parameters.Y.PopulationMean.ConfidenceInterval(0.99).ClosedContains(wald.Shape));
Assert.IsTrue(parameters.X.PopulationVariance.ConfidenceInterval(0.99).ClosedContains(variances.Column(0).Median));
Assert.IsTrue(parameters.Y.PopulationVariance.ConfidenceInterval(0.99).ClosedContains(variances.Column(1).Median));
Assert.IsTrue(parameters.PopulationCovariance.ConfidenceInterval(0.99).ClosedContains(variances.Column(2).Median));
}
public void ExponentialFit()
{
ExponentialDistribution distribution = new ExponentialDistribution(5.0);
Sample sample = SampleTest.CreateSample(distribution, 100);
// fit to normal should be bad
NormalFitResult nfit = NormalDistribution.FitToSample(sample);
Assert.IsTrue(nfit.GoodnessOfFit.Probability < 0.05);
// fit to exponential should be good
ExponentialFitResult efit = ExponentialDistribution.FitToSample(sample);
Assert.IsTrue(efit.GoodnessOfFit.Probability > 0.05);
Assert.IsTrue(efit.Mean.ConfidenceInterval(0.95).ClosedContains(distribution.Mean));
}
public void NormalFit()
{
// pick mu >> sigma so that we get no negative values;
// otherwise the attempt to fit to an exponential will fail
ContinuousDistribution distribution = new NormalDistribution(6.0, 2.0);
Sample sample = SampleTest.CreateSample(distribution, 100);
// fit to normal should be good
NormalFitResult nfit = NormalDistribution.FitToSample(sample);
Assert.IsTrue(nfit.GoodnessOfFit.Probability > 0.05);
Assert.IsTrue(nfit.Mean.ConfidenceInterval(0.95).ClosedContains(distribution.Mean));
Assert.IsTrue(nfit.StandardDeviation.ConfidenceInterval(0.95).ClosedContains(distribution.StandardDeviation));
// fit to exponential should be bad
ExponentialFitResult efit = ExponentialDistribution.FitToSample(sample);
Assert.IsTrue(efit.GoodnessOfFit.Probability < 0.05);
}
public void RayleighFit()
{
RayleighDistribution rayleigh = new RayleighDistribution(3.2);
Sample parameter = new Sample();
Sample variance = new Sample();
for (int i = 0; i < 128; i++)
{
// We pick a quite-small sample, because we have a finite-n unbiased estimator.
Sample s = SampleTest.CreateSample(rayleigh, 8, i);
RayleighFitResult r = RayleighDistribution.FitToSample(s);
parameter.Add(r.Scale.Value);
variance.Add(r.Parameters.VarianceOf("Scale"));
Assert.IsTrue(r.GoodnessOfFit.Probability > 0.01);
}
Assert.IsTrue(parameter.PopulationMean.ConfidenceInterval(0.99).ClosedContains(rayleigh.Scale));
Assert.IsTrue(parameter.PopulationVariance.ConfidenceInterval(0.99).ClosedContains(variance.Median));
}
