public void InverseGaussianSummation()
{
// X_i ~ IG(\mu,\lambda) \rightarrow \sum_{i=0}^{n} X_i ~ IG(n \mu, n^2 \lambda)
Random rng = new Random(0);
WaldDistribution d0 = new WaldDistribution(1.0, 2.0);
Sample s = new Sample();
for (int i = 0; i < 64; i++) {
s.Add(d0.GetRandomValue(rng) + d0.GetRandomValue(rng) + d0.GetRandomValue(rng));
}
WaldDistribution d1 = new WaldDistribution(3.0 * 1.0, 9.0 * 2.0);
TestResult r = s.KolmogorovSmirnovTest(d1);
Console.WriteLine(r.LeftProbability);
}
public void WaldFitUncertainties()
{
WaldDistribution wald = new WaldDistribution(3.5, 2.5);
Random rng = new Random(314159);
BivariateSample P = new BivariateSample();
double cmm = 0.0;
double css = 0.0;
double cms = 0.0;
for (int i = 0; i < 50; i++) {
Sample s = new Sample();
for (int j = 0; j < 50; j++) {
s.Add(wald.GetRandomValue(rng));
}
FitResult r = WaldDistribution.FitToSample(s);
P.Add(r.Parameter(0).Value, r.Parameter(1).Value);
cmm += r.Covariance(0, 0);
css += r.Covariance(1, 1);
cms += r.Covariance(0, 1);
}
cmm /= P.Count;
css /= P.Count;
cms /= P.Count;
Console.WriteLine("{0} {1}", P.X.PopulationMean, P.Y.PopulationMean);
Assert.IsTrue(P.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(wald.Mean));
Assert.IsTrue(P.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(wald.ShapeParameter));
// the ML shape parameter estimate appears to be asymptoticly unbiased, as it must be according to ML fit theory,
// but detectably upward biased for small n. we now correct for this.
Console.WriteLine("{0} {1} {2}", P.X.PopulationVariance, P.Y.PopulationVariance, P.PopulationCovariance);
Console.WriteLine("{0} {1} {2}", cmm, css, cms);
Assert.IsTrue(P.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(cmm));
Assert.IsTrue(P.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(css));
Assert.IsTrue(P.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(cms));
}
