static double GetX(double p, ContinuousDistribution dist)
{
double x, xNext = 1;
do
{
x = xNext;
xNext = x - (dist.CumulativeDistribution(x) - p) /
dist.ProbabilityDensity(x);
}while (Math.Abs(x - xNext) > epsilon);
return(xNext);
}
private void DistributionProbabilityTestHelper(ContinuousDistribution distribution, double x)
{
Console.WriteLine("{0} {1}", distribution.GetType().Name, x);
double P = distribution.LeftProbability(x);
double Q = distribution.RightProbability(x);
Assert.IsTrue((0.0 <= P) && (P <= 1.0));
Assert.IsTrue((0.0 <= Q) && (Q <= 1.0));
Assert.IsTrue(TestUtilities.IsNearlyEqual(P + Q, 1.0));
double p = distribution.ProbabilityDensity(x);
Assert.IsTrue(p >= 0.0);
}
private void DistributionProbabilityTestHelper(ContinuousDistribution distribution, double x)
{
double P = distribution.LeftProbability(x);
double Q = distribution.RightProbability(x);
Assert.IsTrue((0.0 <= P) && (P <= 1.0));
Assert.IsTrue((0.0 <= Q) && (Q <= 1.0));
Assert.IsTrue(TestUtilities.IsNearlyEqual(P + Q, 1.0));
double p = distribution.ProbabilityDensity(x);
Assert.IsTrue(p >= 0.0);
double h = distribution.Hazard(x);
if (p > 0.0 && Q > 0.0)
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(h, p / Q));
}
}
internal static DistributionFitResult <ContinuousDistribution> MaximumLikelihoodFit(IReadOnlyList <double> sample, Func <IReadOnlyList <double>, ContinuousDistribution> factory, IReadOnlyList <double> start, IReadOnlyList <string> names)
{
Debug.Assert(sample != null);
Debug.Assert(factory != null);
Debug.Assert(start != null);
Debug.Assert(names != null);
Debug.Assert(start.Count == names.Count);
// Define a log likelihood function
Func <IReadOnlyList <double>, double> logL = (IReadOnlyList <double> a) => {
ContinuousDistribution d = factory(a);
double lnP = 0.0;
foreach (double value in sample)
{
double P = d.ProbabilityDensity(value);
if (P == 0.0)
{
throw new InvalidOperationException();
}
lnP += Math.Log(P);
}
return(lnP);
};
// Maximize it
MultiExtremum maximum = MultiFunctionMath.FindLocalMaximum(logL, start);
ColumnVector b = maximum.Location;
SymmetricMatrix C = maximum.HessianMatrix;
CholeskyDecomposition CD = C.CholeskyDecomposition();
if (CD == null)
{
throw new DivideByZeroException();
}
C = CD.Inverse();
ContinuousDistribution distribution = factory(maximum.Location);
TestResult test = sample.KolmogorovSmirnovTest(distribution);
return(new ContinuousDistributionFitResult(names, b, C, distribution, test));
}