/// <summary>
/// Gets the Anderson-Darling statistic for the samples and target distribution.
/// </summary>
///
/// <param name="sortedSamples">The sorted samples.</param>
/// <param name="distribution">The target distribution.</param>
///
public static double GetStatistic(double[] sortedSamples, IUnivariateDistribution <double> distribution)
{
double N = sortedSamples.Length;
double S = 0;
int n = sortedSamples.Length;
// Finally, compute the test statistic.
for (int i = 0; i < sortedSamples.Length; i++)
{
double a = 2.0 * (i + 1) - 1;
double b = distribution.DistributionFunction(sortedSamples[i]);
double c = distribution.ComplementaryDistributionFunction(sortedSamples[n - i - 1]);
S += a * (Math.Log(b) + Math.Log(c));
}
return(-n - S / n);
}
/// <summary>
/// Creates a new Anderson-Darling test.
/// </summary>
///
/// <param name="sample">The sample we would like to test as belonging to the <paramref name="hypothesizedDistribution"/>.</param>
/// <param name="hypothesizedDistribution">A fully specified distribution.</param>
///
public AndersonDarlingTest(double[] sample, IUnivariateDistribution hypothesizedDistribution)
{
double N = sample.Length;
// Create the test statistic distribution with given degrees of freedom
this.TheoreticalDistribution = hypothesizedDistribution;
if (hypothesizedDistribution is UniformContinuousDistribution)
{
StatisticDistribution = new AndersonDarlingDistribution(AndersonDarlingDistributionType.Uniform, sample.Length);
}
else if (hypothesizedDistribution is NormalDistribution)
{
StatisticDistribution = new AndersonDarlingDistribution(AndersonDarlingDistributionType.Normal, sample.Length);
}
// Create a copy of the samples to prevent altering the
// constructor's original arguments in the sorting step
double[] Y = (double[])sample.Clone();
// Sort sample
Array.Sort(Y);
// Create the theoretical and empirical distributions
this.TheoreticalDistribution = hypothesizedDistribution;
double S = 0;
int n = Y.Length;
// Finally, compute the test statistic.
for (int i = 0; i < Y.Length; i++)
{
double a = 2.0 * (i + 1) - 1;
double b = TheoreticalDistribution.DistributionFunction(Y[i]);
double c = TheoreticalDistribution.ComplementaryDistributionFunction(Y[n - i - 1]);
S += a * (Math.Log(b) + Math.Log(c));
}
this.Statistic = -n - S / n;
this.PValue = StatisticToPValue(Statistic);
}
