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 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);
}
