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@ -67,16 +67,15 @@ import org.apache.commons.math4.util.MathUtils;
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* default 2-sample test method, {@link #kolmogorovSmirnovTest(double[], double[])} works as
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* follows:
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* <ul>
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* <li>For small samples (where the product of the sample sizes is less than
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* {@value #LARGE_SAMPLE_PRODUCT}), the method presented in [4] is used to compute the
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* exact p-value for the 2-sample test.</li>
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* <li>When the product of the sample sizes exceeds {@value #LARGE_SAMPLE_PRODUCT}, the asymptotic
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* <li>When the product of the sample sizes is less than 10000, the method presented in [4]
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* is used to compute the exact p-value for the 2-sample test.</li>
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* <li>When the product of the sample sizes is larger, the asymptotic
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* distribution of \(D_{n,m}\) is used. See {@link #approximateP(double, int, int)} for details on
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* the approximation.</li>
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* </ul><p>
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* If the product of the sample sizes is less than {@value #LARGE_SAMPLE_PRODUCT} and the sample
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* data contains ties, random jitter is added to the sample data to break ties before applying
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* the algorithm above. Alternatively, the {@link #bootstrap(double[],double[],int,boolean,UniformRandomProvider)}
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* For small samples (former case), if the data contains ties, random jitter is added
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* to the sample data to break ties before applying the algorithm above. Alternatively,
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* the {@link #bootstrap(double[],double[],int,boolean,UniformRandomProvider)}
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* method, modeled after <a href="http://sekhon.berkeley.edu/matching/ks.boot.html">ks.boot</a>
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* in the R Matching package [3], can be used if ties are known to be present in the data.
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* </p>
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@ -187,23 +186,7 @@ public class KolmogorovSmirnovTest {
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* that the {@link #kolmogorovSmirnovStatistic(double[], double[])} associated with a randomly
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* selected partition of the combined sample into subsamples of sizes {@code x.length} and
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* {@code y.length} will strictly exceed (if {@code strict} is {@code true}) or be at least as
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* large as {@code strict = false}) as {@code kolmogorovSmirnovStatistic(x, y)}.
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* <ul>
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* <li>For small samples (where the product of the sample sizes is less than
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* {@value #LARGE_SAMPLE_PRODUCT}), the exact p-value is computed using the method presented
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* in [4], implemented in {@link #exactP(double, int, int, boolean)}. </li>
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* <li>When the product of the sample sizes exceeds {@value #LARGE_SAMPLE_PRODUCT}, the
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* asymptotic distribution of \(D_{n,m}\) is used. See {@link #approximateP(double, int, int)}
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* for details on the approximation.</li>
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* </ul><p>
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* If {@code x.length * y.length <} {@value #LARGE_SAMPLE_PRODUCT} and the combined set of values in
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* {@code x} and {@code y} contains ties, random jitter is added to {@code x} and {@code y} to
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* break ties before computing \(D_{n,m}\) and the p-value. The jitter is uniformly distributed
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* on (-minDelta / 2, minDelta / 2) where minDelta is the smallest pairwise difference between
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* values in the combined sample.</p>
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* <p>
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* If ties are known to be present in the data, {@link #bootstrap(double[],double[],int,boolean,UniformRandomProvider)}
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* may be used as an alternative method for estimating the p-value.</p>
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* large as (if {@code strict} is {@code false}) as {@code kolmogorovSmirnovStatistic(x, y)}.
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*
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* @param x first sample dataset.
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* @param y second sample dataset.
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@ -215,6 +198,7 @@ public class KolmogorovSmirnovTest {
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* not have length at least 2.
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* @throws NullArgumentException if either {@code x} or {@code y} is null.
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* @throws NotANumberException if the input arrays contain NaN values.
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*
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* @see #bootstrap(double[],double[],int,boolean,UniformRandomProvider)
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*/
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public double kolmogorovSmirnovTest(double[] x, double[] y, boolean strict) {
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@ -969,9 +953,7 @@ public class KolmogorovSmirnovTest {
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* <p>
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* Specifically, what is returned is \(1 - k(d \sqrt{mn / (m + n)})\) where \(k(t) = 1 + 2
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* \sum_{i=1}^\infty (-1)^i e^{-2 i^2 t^2}\). See {@link #ksSum(double, double, int)} for
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* details on how convergence of the sum is determined. This implementation passes {@code ksSum}
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* {@value #KS_SUM_CAUCHY_CRITERION} as {@code tolerance} and
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* {@value #MAXIMUM_PARTIAL_SUM_COUNT} as {@code maxIterations}.
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* details on how convergence of the sum is determined.
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* </p>
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*
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* @param d D-statistic value
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