/// <summary>
/// Creates a new One-Sample Lilliefors' Kolmogorov-Smirnov 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 (which could have been estimated from the data).</param>
/// <param name="alternate">The alternative hypothesis (research hypothesis) to test.</param>
/// <param name="iterations">The number of Monte-Carlo iterations to perform. Default is 10,000.</param>
/// <param name="reestimate">Whether the target distribution should be re-estimated from the sampled data
/// at each Monte-Carlo iteration. Pass true in case <paramref name="hypothesizedDistribution"/> has been
/// estimated from the data.</param>
///
public LillieforsTest(double[] sample, ISampleableDistribution <double> hypothesizedDistribution,
KolmogorovSmirnovTestHypothesis alternate = KolmogorovSmirnovTestHypothesis.SampleIsDifferent,
int iterations = 10000, bool reestimate = true)
: this()
{
if (reestimate)
{
if (!(hypothesizedDistribution is IFittableDistribution <double>))
{
throw new InvalidOperationException("The estimate option can only be used with distributions that implement IFittableDistribution<double>.");
}
}
this.Hypothesis = alternate;
// Create a copy of the samples to prevent altering the
// constructor's original arguments in the sorting step
double[] orderedSamples = sample.Sorted();
// Create the theoretical and empirical distributions
this.TheoreticalDistribution = hypothesizedDistribution;
this.EmpiricalDistribution = new EmpiricalDistribution(orderedSamples, smoothing: 0);
this.NumberOfSamples = sample.Length;
StatisticDistribution = GetSimulatedDistribution(hypothesizedDistribution,
reestimate, iterations, alternate);
// Finally, compute the test statistic and perform actual testing.
base.Statistic = KolmogorovSmirnovTest.GetStatistic(orderedSamples, TheoreticalDistribution, alternate);
this.Tail = (DistributionTail)alternate;
base.PValue = StatisticToPValue(Statistic);
}
/// <summary>
/// Creates a new One-Sample Kolmogorov 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 (which must NOT have been estimated from the data).</param>
/// <param name="alternate">The alternative hypothesis (research hypothesis) to test.</param>
///
public KolmogorovSmirnovTest(double[] sample, IDistribution <double> hypothesizedDistribution,
KolmogorovSmirnovTestHypothesis alternate = KolmogorovSmirnovTestHypothesis.SampleIsDifferent)
{
this.Hypothesis = alternate;
// Create the test statistic distribution with given degrees of freedom
StatisticDistribution = new KolmogorovSmirnovDistribution(sample.Length);
// Create a copy of the samples to prevent altering the
// constructor's original arguments in the sorting step
double[] sortedSamples = sample.Sorted();
// Create the theoretical and empirical distributions
this.TheoreticalDistribution = hypothesizedDistribution;
this.EmpiricalDistribution = new EmpiricalDistribution(sortedSamples, smoothing: 0);
// Finally, compute the test statistic and perform actual testing.
base.Statistic = GetStatistic(sortedSamples, TheoreticalDistribution, alternate);
this.Tail = (DistributionTail)alternate;
base.PValue = StatisticToPValue(Statistic);
}
/// <summary>
/// Gets the appropriate Kolmogorov-Sminorv D statistic for the samples and target distribution.
/// </summary>
///
/// <param name="sortedSamples">The sorted samples.</param>
/// <param name="distribution">The target distribution.</param>
/// <param name="alternate">The alternate hypothesis for the KS test. For <see cref="KolmogorovSmirnovTestHypothesis.SampleIsDifferent"/>, this
/// is the two-sided Dn statistic; for <see cref="KolmogorovSmirnovTestHypothesis.SampleIsGreater"/> this is the one sided Dn+ statistic;
/// and for <see cref="KolmogorovSmirnovTestHypothesis.SampleIsSmaller"/> this is the one sided Dn- statistic.</param>
///
public static double GetStatistic(double[] sortedSamples, IDistribution <double> distribution, KolmogorovSmirnovTestHypothesis alternate)
{
// Finally, compute the test statistic and perform actual testing.
switch (alternate)
{
case KolmogorovSmirnovTestHypothesis.SampleIsDifferent:
return(TwoSide(sortedSamples, distribution));
case KolmogorovSmirnovTestHypothesis.SampleIsGreater:
return(OneSideUpper(sortedSamples, distribution));
case KolmogorovSmirnovTestHypothesis.SampleIsSmaller:
return(OneSideLower(sortedSamples, distribution));
}
throw new ArgumentOutOfRangeException("alternate");
}
/// <summary>
/// Creates a new One-Sample Kolmogorov 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 (which must NOT have been estimated from the data).</param>
/// <param name="alternate">The alternative hypothesis (research hypothesis) to test.</param>
///
public KolmogorovSmirnovTest(double[] sample, UnivariateContinuousDistribution hypothesizedDistribution,
KolmogorovSmirnovTestHypothesis alternate = KolmogorovSmirnovTestHypothesis.SampleIsDifferent)
{
this.Hypothesis = alternate;
double N = sample.Length;
// Create the test statistic distribution with given degrees of freedom
StatisticDistribution = new KolmogorovSmirnovDistribution(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();
double[] D = new double[sample.Length];
// Sort sample
Array.Sort(Y);
// Create the theoretical and empirical distributions
this.TheoreticalDistribution = hypothesizedDistribution;
this.EmpiricalDistribution = new EmpiricalDistribution(Y, smoothing: 0);
Func <double, double> F = TheoreticalDistribution.DistributionFunction;
// Finally, compute the test statistic and perform actual testing.
if (alternate == KolmogorovSmirnovTestHypothesis.SampleIsDifferent)
{
// Test if the sample's distribution is just significantly
// "different" than the given theoretical distribution.
// This is a correction on the common formulation found in many places
// such as in Wikipedia. Please see the Engineering Statistics Handbook,
// section "1.3.5.16. Kolmogorov-Smirnov Goodness-of-Fit Test" for more
// details: http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm
for (int i = 0; i < sample.Length; i++)
{
D[i] = Math.Max(Math.Abs(F(Y[i]) - i / N), Math.Abs((i + 1) / N - F(Y[i])));
}
base.Statistic = D.Max(); // This is the two-sided "Dn" statistic.
base.PValue = StatisticDistribution.ComplementaryDistributionFunction(Statistic);
base.Tail = Testing.DistributionTail.TwoTail;
}
else if (alternate == KolmogorovSmirnovTestHypothesis.SampleIsGreater)
{
// Test if the sample's distribution is "larger" than the
// given theoretical distribution, in a statistical sense.
for (int i = 0; i < sample.Length; i++)
{
D[i] = Math.Max(i / N - F(Y[i]), (i + 1) / N - F(Y[i]));
}
base.Statistic = D.Max(); // This is the one-sided "Dn+" statistic.
base.PValue = StatisticDistribution.OneSideDistributionFunction(Statistic);
base.Tail = Testing.DistributionTail.OneUpper;
}
else
{
// Test if the sample's distribution is "smaller" than the
// given theoretical distribution, in a statistical sense.
for (int i = 0; i < sample.Length; i++)
{
D[i] = Math.Max(F(Y[i]) - i / N, F(Y[i]) - (i + 1) / N);
}
base.Statistic = D.Max(); // This is the one-sided "Dn-" statistic.
base.PValue = StatisticDistribution.OneSideDistributionFunction(Statistic);
base.Tail = Testing.DistributionTail.OneLower;
}
}
private EmpiricalDistribution GetSimulatedDistribution(ISampleableDistribution <double> hypothesizedDistribution,
bool reestimate, int iterations, KolmogorovSmirnovTestHypothesis alternate)
{
double[] samples = new double[iterations];
if (reestimate)
{
Parallel.For(0, iterations, i =>
{
double[] s = hypothesizedDistribution.Generate(samples: NumberOfSamples);
Vector.Sort <double>(s);
var fittable = (IFittableDistribution <double>)hypothesizedDistribution.Clone();
fittable.Fit(s);
samples[i] = KolmogorovSmirnovTest.GetStatistic((double[])s, (IDistribution <double>)fittable, alternate);
});
}
else
{
Parallel.For(0, iterations, i =>
{
double[] s = hypothesizedDistribution.Generate(samples: NumberOfSamples);
Vector.Sort <double>(s);
samples[i] = KolmogorovSmirnovTest.GetStatistic((double[])s, (IDistribution <double>)hypothesizedDistribution, alternate);
});
}
return(new EmpiricalDistribution(samples, smoothing: 0));
}
