public void NormalFitCovariances()
{
NormalDistribution N = new NormalDistribution(-1.0, 2.0);
// Create a bivariate sample to hold our fitted best mu and sigma values
// so we can determine their covariance as well as their means and variances
BivariateSample parameters = new BivariateSample();
MultivariateSample covariances = new MultivariateSample(3);
// A bunch of times, create a normal sample
for (int i = 0; i < 128; i++)
{
// We use small samples so the variation in mu and sigma will be more substantial.
Sample s = TestUtilities.CreateSample(N, 8, i);
// Fit each sample to a normal distribution
NormalFitResult fit = NormalDistribution.FitToSample(s);
// and record the mu and sigma values from the fit into our bivariate sample
parameters.Add(fit.Mean.Value, fit.StandardDeviation.Value);
// also record the claimed covariances among these parameters
covariances.Add(fit.Parameters.CovarianceMatrix[0, 0], fit.Parameters.CovarianceMatrix[1, 1], fit.Parameters.CovarianceMatrix[0, 1]);
}
// the mean fit values should agree with the population distribution
Assert.IsTrue(parameters.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(N.Mean));
Assert.IsTrue(parameters.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(N.StandardDeviation));
// but also the covariances of those fit values should agree with the claimed covariances
Assert.IsTrue(parameters.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(covariances.Column(0).Mean));
Assert.IsTrue(parameters.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(covariances.Column(1).Mean));
Assert.IsTrue(parameters.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(covariances.Column(2).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);
}
