public void DistributionCentralMomentIntegral()
{
foreach (ContinuousDistribution distribution in distributions)
{
foreach (int n in TestUtilities.GenerateIntegerValues(2, 24, 8))
{
// get the predicted central moment
double C = distribution.CentralMoment(n);
// don't try to integrate infinite moments
if (Double.IsInfinity(C) || Double.IsNaN(C))
{
continue;
}
if (C == 0.0)
{
continue;
}
IntegrationSettings settings = new IntegrationSettings();
if (C == 0.0)
{
// if moment is zero, use absolute precision
settings.AbsolutePrecision = TestUtilities.TargetPrecision;
settings.RelativePrecision = 0.0;
}
else
{
// if moment in non-zero, use relative precision
settings.AbsolutePrecision = 0.0;
settings.RelativePrecision = TestUtilities.TargetPrecision;
}
// do the integral
double m = distribution.Mean;
Func <double, double> f = delegate(double x) {
return(distribution.ProbabilityDensity(x) * MoreMath.Pow(x - m, n));
};
try {
double CI = FunctionMath.Integrate(f, distribution.Support, settings).Value;
Console.WriteLine("{0} {1} {2} {3}", distribution.GetType().Name, n, C, CI);
if (C == 0.0)
{
Assert.IsTrue(Math.Abs(CI) < TestUtilities.TargetPrecision);
}
else
{
double e = TestUtilities.TargetPrecision;
// reduce required precision, because some distributions (e.g. Kolmogorov, Weibull)
// have no analytic expressions for central moments, which must therefore be
// determined via raw moments and are thus subject to cancelation error
// can we revisit this later?
if (distribution is WeibullDistribution)
{
e = Math.Sqrt(Math.Sqrt(e));
}
if (distribution is KolmogorovDistribution)
{
e = Math.Sqrt(e);
}
if (distribution is KuiperDistribution)
{
e = Math.Sqrt(Math.Sqrt(e));
}
if (distribution is TriangularDistribution)
{
e = Math.Sqrt(e);
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(C, CI, e));
}
} catch (NonconvergenceException) {
Console.WriteLine("{0} {1} {2} {3}", distribution.GetType().Name, n, C, "NC");
// deal with these later; they are integration problems, not distribution problems
}
}
}
}
