[MATH-1197] Computation of 2-sample KS statistic was wrong in case of ties.
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Thomas Neidhart
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8ed40d5302
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a6abb8b003
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@ -54,6 +54,10 @@ If the output is not quite correct, check for invisible trailing spaces!
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</release>
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<release version="4.0" date="XXXX-XX-XX" description="">
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<action dev="tn" type="fix" issue="MATH-1197">
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Computation of 2-sample Kolmogoriv-Smirnov statistic in case of ties
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was not correct.
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</action>
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<action dev="tn" type="remove" issue="MATH-1205">
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Removed methods "test(...)" from "AbstractUnivariateStatistic".
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The already existing methods "MathArrays#verifyValues(...)" shall
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@ -298,9 +298,13 @@ public class KolmogorovSmirnovTest {
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double supD = 0d;
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// First walk x points
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for (int i = 0; i < n; i++) {
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final double cdf_x = (i + 1d) / n;
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final int yIndex = Arrays.binarySearch(sy, sx[i]);
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final double cdf_y = yIndex >= 0 ? (yIndex + 1d) / m : (-yIndex - 1d) / m;
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final double x_i = sx[i];
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// ties can be safely ignored
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if (i > 0 && x_i == sx[i-1]) {
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continue;
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}
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final double cdf_x = edf(x_i, sx);
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final double cdf_y = edf(x_i, sy);
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final double curD = FastMath.abs(cdf_x - cdf_y);
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if (curD > supD) {
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supD = curD;
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@ -308,9 +312,13 @@ public class KolmogorovSmirnovTest {
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}
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// Now look at y
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for (int i = 0; i < m; i++) {
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final double cdf_y = (i + 1d) / m;
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final int xIndex = Arrays.binarySearch(sx, sy[i]);
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final double cdf_x = xIndex >= 0 ? (xIndex + 1d) / n : (-xIndex - 1d) / n;
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final double y_i = sy[i];
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// ties can be safely ignored
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if (i > 0 && y_i == sy[i-1]) {
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continue;
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}
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final double cdf_x = edf(y_i, sx);
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final double cdf_y = edf(y_i, sy);
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final double curD = FastMath.abs(cdf_x - cdf_y);
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if (curD > supD) {
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supD = curD;
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@ -319,6 +327,24 @@ public class KolmogorovSmirnovTest {
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return supD;
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}
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/**
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* Computes the empirical distribution function.
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*
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* @param x the given x
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* @param samples the observations
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* @return the empirical distribution function \(F_n(x)\)
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*/
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private double edf(final double x, final double[] samples) {
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final int n = samples.length;
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int index = Arrays.binarySearch(samples, x);
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if (index >= 0) {
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while(index < (n - 1) && samples[index+1] == x) {
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++index;
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}
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}
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return index >= 0 ? (index + 1d) / n : (-index - 1d) / n;
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}
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/**
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* Computes the <i>p-value</i>, or <i>observed significance level</i>, of a one-sample <a
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* href="http://en.wikipedia.org/wiki/Kolmogorov-Smirnov_test"> Kolmogorov-Smirnov test</a>
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@ -429,7 +455,7 @@ public class KolmogorovSmirnovTest {
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return 1;
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}
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if (exact) {
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return exactK(d,n);
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return exactK(d, n);
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}
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if (n <= 140) {
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return roundedK(d, n);
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@ -501,7 +527,6 @@ public class KolmogorovSmirnovTest {
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* @since 3.4
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*/
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public double pelzGood(double d, int n) {
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// Change the variable since approximation is for the distribution evaluated at d / sqrt(n)
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final double sqrtN = FastMath.sqrt(n);
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final double z = d * sqrtN;
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@ -834,8 +859,13 @@ public class KolmogorovSmirnovTest {
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* @throws TooManyIterationsException if the series does not converge
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*/
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public double ksSum(double t, double tolerance, int maxIterations) {
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if (t == 0.0) {
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return 1.0;
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}
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// TODO: for small t (say less than 1), the alternative expansion in part 3 of [1]
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// from class javadoc should be used.
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final double x = -2 * t * t;
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int sign = -1;
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long i = 1;
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@ -926,7 +956,8 @@ public class KolmogorovSmirnovTest {
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public double approximateP(double d, int n, int m) {
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final double dm = m;
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final double dn = n;
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return 1 - ksSum(d * FastMath.sqrt((dm * dn) / (dm + dn)), KS_SUM_CAUCHY_CRITERION, MAXIMUM_PARTIAL_SUM_COUNT);
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return 1 - ksSum(d * FastMath.sqrt((dm * dn) / (dm + dn)),
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KS_SUM_CAUCHY_CRITERION, MAXIMUM_PARTIAL_SUM_COUNT);
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}
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/**
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@ -27,7 +27,7 @@ import org.junit.Test;
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/**
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* Test cases for {@link KolmogorovSmirnovTest}.
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*
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*
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* @since 3.3
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*/
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public class KolmogorovSmirnovTestTest {
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@ -221,7 +221,7 @@ public class KolmogorovSmirnovTestTest {
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}
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}
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}
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@Test
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public void testPelzGoodApproximation() {
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KolmogorovSmirnovTest ksTest = new KolmogorovSmirnovTest();
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@ -237,7 +237,7 @@ public class KolmogorovSmirnovTestTest {
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0.9999999999999877, 0.9999999999999191, 0.9999999999999254, 0.9999999999998178, 0.9999999999917788,
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0.9999999999998556, 0.9999999999992014, 0.9999999999988859, 0.9999999999999325, 0.9999999999821726
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};
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final double tol = 10e-15;
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int k = 0;
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for (int i = 0; i < 6; i++) {
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@ -255,13 +255,13 @@ public class KolmogorovSmirnovTestTest {
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Assert.assertEquals(0.0319983962391632, test.kolmogorovSmirnovTest(gaussian, gaussian2), TOLERANCE);
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Assert.assertEquals(0.202352941176471, test.kolmogorovSmirnovStatistic(gaussian, gaussian2), TOLERANCE);
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}
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/**
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/**
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* MATH-1181
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* Verify that large sample method is selected for sample product > Integer.MAX_VALUE
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* (integer overflow in sample product)
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*/
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@Test(timeout=5000)
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@Test//(timeout=5000)
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public void testTwoSampleProductSizeOverflow() {
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final int n = 50000;
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Assert.assertTrue(n * n < 0);
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@ -270,7 +270,7 @@ public class KolmogorovSmirnovTestTest {
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final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest();
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Assert.assertFalse(Double.isNaN(test.kolmogorovSmirnovTest(x, y)));
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}
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/**
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* Verifies that Monte Carlo simulation gives results close to exact p values. This test is a
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@ -303,15 +303,78 @@ public class KolmogorovSmirnovTestTest {
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}
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}
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@Test
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public void testTwoSampleWithManyTies() {
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// MATH-1197
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final double[] x = {
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653,
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2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653,
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2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653,
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2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653,
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2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653,
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2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653,
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3.181199, 3.181199, 3.181199, 3.181199, 3.181199, 3.181199,
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3.723539, 3.723539, 3.723539, 3.723539, 4.383482, 4.383482,
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4.383482, 4.383482, 5.320671, 5.320671, 5.320671, 5.717284,
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6.964001, 7.352165, 8.710510, 8.710510, 8.710510, 8.710510,
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8.710510, 8.710510, 9.539004, 9.539004, 10.720619, 17.726077,
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17.726077, 17.726077, 17.726077, 22.053875, 23.799144, 27.355308,
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30.584960, 30.584960, 30.584960, 30.584960, 30.751808
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};
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final double[] y = {
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000, 2.202653, 2.202653, 2.202653,
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2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 3.061758,
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3.723539, 5.628420, 5.628420, 5.628420, 5.628420, 5.628420,
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6.916982, 6.916982, 6.916982, 10.178538, 10.178538, 10.178538,
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10.178538, 10.178538
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};
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final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest();
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Assert.assertEquals(0.0640394088, test.kolmogorovSmirnovStatistic(x, y), 1e-6);
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Assert.assertEquals(0.9792777290, test.kolmogorovSmirnovTest(x, y), 1e-6);
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}
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/**
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* Verifies the inequality exactP(criticalValue, n, m, true) < alpha < exactP(criticalValue, n,
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* m, false).
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*
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*
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* Note that the validity of this check depends on the fact that alpha lies strictly between two
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* attained values of the distribution and that criticalValue is one of the attained values. The
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* critical value table (reference below) uses attained values. This test therefore also
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* verifies that criticalValue is attained.
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*
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*
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* @param n first sample size
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* @param m second sample size
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* @param criticalValue critical value
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@ -325,7 +388,7 @@ public class KolmogorovSmirnovTestTest {
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/**
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* Verifies that approximateP(criticalValue, n, m) is within epsilon of alpha.
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*
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*
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* @param n first sample size
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* @param m second sample size
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* @param criticalValue critical value (from table)
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@ -336,5 +399,5 @@ public class KolmogorovSmirnovTestTest {
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final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest();
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Assert.assertEquals(alpha, test.approximateP(criticalValue, n, m), epsilon);
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}
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}
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