| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| package org.apache.commons.math3.stat.inference; |
| |
| import java.lang.reflect.Method; |
| import java.util.Arrays; |
| |
| import org.apache.commons.math3.TestUtils; |
| import org.apache.commons.math3.distribution.NormalDistribution; |
| import org.apache.commons.math3.distribution.UniformRealDistribution; |
| import org.apache.commons.math3.random.RandomGenerator; |
| import org.apache.commons.math3.random.Well19937c; |
| import org.apache.commons.math3.util.CombinatoricsUtils; |
| import org.apache.commons.math3.util.FastMath; |
| import org.apache.commons.math3.util.MathArrays; |
| import org.junit.Assert; |
| import org.junit.Test; |
| |
| /** |
| * Test cases for {@link KolmogorovSmirnovTest}. |
| * |
| * @since 3.3 |
| */ |
| public class KolmogorovSmirnovTestTest { |
| |
| protected static final double TOLERANCE = 10e-10; |
| |
| // Random N(0,1) values generated using R rnorm |
| protected static final double[] gaussian = { |
| 0.26055895, -0.63665233, 1.51221323, 0.61246988, -0.03013003, -1.73025682, -0.51435805, 0.70494168, 0.18242945, |
| 0.94734336, -0.04286604, -0.37931719, -1.07026403, -2.05861425, 0.11201862, 0.71400136, -0.52122185, |
| -0.02478725, -1.86811649, -1.79907688, 0.15046279, 1.32390193, 1.55889719, 1.83149171, -0.03948003, |
| -0.98579207, -0.76790540, 0.89080682, 0.19532153, 0.40692841, 0.15047336, -0.58546562, -0.39865469, 0.77604271, |
| -0.65188221, -1.80368554, 0.65273365, -0.75283102, -1.91022150, -0.07640869, -1.08681188, -0.89270600, |
| 2.09017508, 0.43907981, 0.10744033, -0.70961218, 1.15707300, 0.44560525, -2.04593349, 0.53816843, -0.08366640, |
| 0.24652218, 1.80549401, -0.99220707, -1.14589408, -0.27170290, -0.49696855, 0.00968353, -1.87113545, |
| -1.91116529, 0.97151891, -0.73576115, -0.59437029, 0.72148436, 0.01747695, -0.62601157, -1.00971538, |
| -1.42691397, 1.03250131, -0.30672627, -0.15353992, -1.19976069, -0.68364218, 0.37525652, -0.46592881, |
| -0.52116168, -0.17162202, 1.04679215, 0.25165971, -0.04125231, -0.23756244, -0.93389975, 0.75551407, |
| 0.08347445, -0.27482228, -0.4717632, -0.1867746, -0.1166976, 0.5763333, 0.1307952, 0.7630584, -0.3616248, |
| 2.1383790, -0.7946630, 0.0231885, 0.7919195, 1.6057144, -0.3802508, 0.1229078, 1.5252901, -0.8543149, 0.3025040 |
| }; |
| |
| // Random N(0, 1.6) values generated using R rnorm |
| protected static final double[] gaussian2 = { |
| 2.88041498038308, -0.632349445671017, 0.402121295225571, 0.692626364613243, 1.30693446815426, |
| -0.714176317131286, -0.233169206599583, 1.09113298322107, -1.53149079994305, 1.23259966205809, |
| 1.01389927412503, 0.0143898711497477, -0.512813545447559, 2.79364360835469, 0.662008875538092, |
| 1.04861546834788, -0.321280099931466, 0.250296656278743, 1.75820367603736, -2.31433523590905, |
| -0.462694696086403, 0.187725700950191, -2.24410950019152, 2.83473751105445, 0.252460174391016, |
| 1.39051945380281, -1.56270144203134, 0.998522814471644, -1.50147469080896, 0.145307533554146, |
| 0.469089457043406, -0.0914780723809334, -0.123446939266548, -0.610513388160565, -3.71548343891957, |
| -0.329577317349478, -0.312973794075871, 2.02051909758923, 2.85214308266271, 0.0193222002327237, |
| -0.0322422268266562, 0.514736012106768, 0.231484953375887, -2.22468798953629, 1.42197716075595, |
| 2.69988043856357, 0.0443757119128293, 0.721536984407798, -0.0445688839903234, -0.294372724550705, |
| 0.234041580912698, -0.868973119365727, 1.3524893453845, -0.931054600134503, -0.263514296006792, |
| 0.540949457402918, -0.882544288773685, -0.34148675747989, 1.56664494810034, 2.19850536566584, |
| -0.667972122928022, -0.70889669526203, -0.00251758193079668, 2.39527162977682, -2.7559594317269, |
| -0.547393502656671, -2.62144031572617, 2.81504147017922, -1.02036850201042, -1.00713927602786, |
| -0.520197775122254, 1.00625480138649, 2.46756916531313, 1.64364743727799, 0.704545210648595, |
| -0.425885789416992, -1.78387854908546, -0.286783886710481, 0.404183648369076, -0.369324280845769, |
| -0.0391185138840443, 2.41257787857293, 2.49744281317859, -0.826964496939021, -0.792555379958975, |
| 1.81097685787403, -0.475014580016638, 1.23387615291805, 0.646615294802053, 1.88496377454523, 1.20390698380814, |
| -0.27812153371728, 2.50149494533101, 0.406964323253817, -1.72253451309982, 1.98432494184332, 2.2223658560333, |
| 0.393086362404685, -0.504073151377089, -0.0484610869883821 |
| }; |
| |
| // Random uniform (0, 1) generated using R runif |
| protected static final double[] uniform = { |
| 0.7930305, 0.6424382, 0.8747699, 0.7156518, 0.1845909, 0.2022326, 0.4877206, 0.8928752, 0.2293062, 0.4222006, |
| 0.1610459, 0.2830535, 0.9946345, 0.7329499, 0.26411126, 0.87958133, 0.29827437, 0.39185988, 0.38351185, |
| 0.36359611, 0.48646472, 0.05577866, 0.56152250, 0.52672013, 0.13171783, 0.95864085, 0.03060207, 0.33514887, |
| 0.72508148, 0.38901437, 0.9978665, 0.5981300, 0.1065388, 0.7036991, 0.1071584, 0.4423963, 0.1107071, 0.6437221, |
| 0.58523872, 0.05044634, 0.65999539, 0.37367260, 0.73270024, 0.47473755, 0.74661163, 0.50765549, 0.05377347, |
| 0.40998009, 0.55235182, 0.21361998, 0.63117971, 0.18109222, 0.89153510, 0.23203248, 0.6177106, 0.6856418, |
| 0.2158557, 0.9870501, 0.2036914, 0.2100311, 0.9065020, 0.7459159, 0.56631790, 0.06753629, 0.39684629, |
| 0.52504615, 0.14199103, 0.78551120, 0.90503321, 0.80452362, 0.9960115, 0.8172592, 0.5831134, 0.8794187, |
| 0.2021501, 0.2923505, 0.9561824, 0.8792248, 0.85201008, 0.02945562, 0.26200374, 0.11382818, 0.17238856, |
| 0.36449473, 0.69688273, 0.96216330, 0.4859432, 0.4503438, 0.1917656, 0.8357845, 0.9957812, 0.4633570, |
| 0.8654599, 0.4597996, 0.68190289, 0.58887855, 0.09359396, 0.98081979, 0.73659533, 0.89344777, 0.18903099, |
| 0.97660425 |
| }; |
| |
| /** Unit normal distribution, unit normal data */ |
| @Test |
| public void testOneSampleGaussianGaussian() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| final NormalDistribution unitNormal = new NormalDistribution(0d, 1d); |
| // Uncomment to run exact test - takes about a minute. Same value is used in R tests and for |
| // approx. |
| // Assert.assertEquals(0.3172069207622391, test.kolmogorovSmirnovTest(unitNormal, gaussian, |
| // true), TOLERANCE); |
| Assert.assertEquals(0.3172069207622391, test.kolmogorovSmirnovTest(unitNormal, gaussian, false), TOLERANCE); |
| Assert.assertFalse(test.kolmogorovSmirnovTest(unitNormal, gaussian, 0.05)); |
| Assert.assertEquals(0.0932947561266756, test.kolmogorovSmirnovStatistic(unitNormal, gaussian), TOLERANCE); |
| } |
| |
| /** Unit normal distribution, unit normal data, small dataset */ |
| @Test |
| public void testOneSampleGaussianGaussianSmallSample() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| final NormalDistribution unitNormal = new NormalDistribution(0d, 1d); |
| final double[] shortGaussian = new double[50]; |
| System.arraycopy(gaussian, 0, shortGaussian, 0, 50); |
| Assert.assertEquals(0.683736463728347, test.kolmogorovSmirnovTest(unitNormal, shortGaussian, false), TOLERANCE); |
| Assert.assertFalse(test.kolmogorovSmirnovTest(unitNormal, gaussian, 0.05)); |
| Assert.assertEquals(0.09820779969463278, test.kolmogorovSmirnovStatistic(unitNormal, shortGaussian), TOLERANCE); |
| } |
| |
| /** Unit normal distribution, uniform data */ |
| @Test |
| public void testOneSampleGaussianUniform() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| final NormalDistribution unitNormal = new NormalDistribution(0d, 1d); |
| // Uncomment to run exact test - takes a long time. Same value is used in R tests and for |
| // approx. |
| // Assert.assertEquals(0.3172069207622391, test.kolmogorovSmirnovTest(unitNormal, uniform, |
| // true), TOLERANCE); |
| Assert.assertEquals(8.881784197001252E-16, test.kolmogorovSmirnovTest(unitNormal, uniform, false), TOLERANCE); |
| Assert.assertFalse(test.kolmogorovSmirnovTest(unitNormal, gaussian, 0.05)); |
| Assert.assertEquals(0.5117493931609258, test.kolmogorovSmirnovStatistic(unitNormal, uniform), TOLERANCE); |
| } |
| |
| /** Uniform distribution, uniform data */ |
| // @Test - takes about 6 seconds, uncomment for |
| public void testOneSampleUniformUniform() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| final UniformRealDistribution unif = new UniformRealDistribution(-0.5, 0.5); |
| Assert.assertEquals(8.881784197001252E-16, test.kolmogorovSmirnovTest(unif, uniform, false), TOLERANCE); |
| Assert.assertTrue(test.kolmogorovSmirnovTest(unif, uniform, 0.05)); |
| Assert.assertEquals(0.5400666982352942, test.kolmogorovSmirnovStatistic(unif, uniform), TOLERANCE); |
| } |
| |
| /** Uniform distribution, uniform data, small dataset */ |
| @Test |
| public void testOneSampleUniformUniformSmallSample() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| final UniformRealDistribution unif = new UniformRealDistribution(-0.5, 0.5); |
| final double[] shortUniform = new double[20]; |
| System.arraycopy(uniform, 0, shortUniform, 0, 20); |
| Assert.assertEquals(4.117594598618268E-9, test.kolmogorovSmirnovTest(unif, shortUniform, false), TOLERANCE); |
| Assert.assertTrue(test.kolmogorovSmirnovTest(unif, shortUniform, 0.05)); |
| Assert.assertEquals(0.6610459, test.kolmogorovSmirnovStatistic(unif, shortUniform), TOLERANCE); |
| } |
| |
| /** Uniform distribution, unit normal dataset */ |
| @Test |
| public void testOneSampleUniformGaussian() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| final UniformRealDistribution unif = new UniformRealDistribution(-0.5, 0.5); |
| // Value was obtained via exact test, validated against R. Running exact test takes a long |
| // time. |
| Assert.assertEquals(4.9405812774239166E-11, test.kolmogorovSmirnovTest(unif, gaussian, false), TOLERANCE); |
| Assert.assertTrue(test.kolmogorovSmirnovTest(unif, gaussian, 0.05)); |
| Assert.assertEquals(0.3401058049019608, test.kolmogorovSmirnovStatistic(unif, gaussian), TOLERANCE); |
| } |
| |
| /** Small samples - exact p-value, checked against R */ |
| @Test |
| public void testTwoSampleSmallSampleExact() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| final double[] smallSample1 = { |
| 6, 7, 9, 13, 19, 21, 22, 23, 24 |
| }; |
| final double[] smallSample2 = { |
| 10, 11, 12, 16, 20, 27, 28, 32, 44, 54 |
| }; |
| // Reference values from R, version 3.2.0 - R uses non-strict inequality in null hypothesis |
| Assert |
| .assertEquals(0.105577085453247, test.kolmogorovSmirnovTest(smallSample1, smallSample2, false), TOLERANCE); |
| Assert.assertEquals(0.5, test.kolmogorovSmirnovStatistic(smallSample1, smallSample2), TOLERANCE); |
| } |
| |
| /** Small samples - exact p-value, checked against R */ |
| @Test |
| public void testTwoSampleSmallSampleExact2() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| final double[] smallSample1 = { |
| 6, 7, 9, 13, 19, 21, 22, 23, 24, 29, 30, 34, 36, 41, 45, 47, 51, 63, 33, 91 |
| }; |
| final double[] smallSample2 = { |
| 10, 11, 12, 16, 20, 27, 28, 32, 44, 54, 56, 57, 64, 69, 71, 80, 81, 88, 90 |
| }; |
| // Reference values from R, version 3.2.0 - R uses non-strict inequality in null hypothesis |
| Assert |
| .assertEquals(0.0462986609, test.kolmogorovSmirnovTest(smallSample1, smallSample2, false), TOLERANCE); |
| Assert.assertEquals(0.4263157895, test.kolmogorovSmirnovStatistic(smallSample1, smallSample2), TOLERANCE); |
| } |
| |
| /** Small samples - exact p-value, checked against R */ |
| @Test |
| public void testTwoSampleSmallSampleExact3() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| final double[] smallSample1 = { |
| -10, -5, 17, 21, 22, 23, 24, 30, 44, 50, 56, 57, 59, 67, 73, 75, 77, 78, 79, 80, 81, 83, 84, 85, 88, 90, |
| 92, 93, 94, 95, 98, 100, 101, 103, 105, 110 |
| }; |
| final double[] smallSample2 = { |
| -2, -1, 0, 10, 14, 15, 16, 20, 25, 26, 27, 31, 32, 33, 34, 45, 47, 48, 51, 52, 53, 54, 60, 61, 62, 63, |
| 74, 82, 106, 107, 109, 11, 112, 113, 114 |
| }; |
| // Reference values from R, version 3.2.0 - R uses non-strict inequality in null hypothesis |
| Assert |
| .assertEquals(0.00300743602, test.kolmogorovSmirnovTest(smallSample1, smallSample2, false), TOLERANCE); |
| Assert.assertEquals(0.4103174603, test.kolmogorovSmirnovStatistic(smallSample1, smallSample2), TOLERANCE); |
| Assert |
| .assertEquals(0.00300743602, test.kolmogorovSmirnovTest(smallSample2, smallSample1, false), TOLERANCE); |
| } |
| |
| /** |
| * Checks exact p-value computations using critical values from Table 9 in V.K Rohatgi, An |
| * Introduction to Probability and Mathematical Statistics, Wiley, 1976, ISBN 0-471-73135-8. |
| */ |
| @Test |
| public void testTwoSampleExactP() { |
| checkExactTable(4, 6, 5d / 6d, 0.01d); |
| checkExactTable(4, 7, 17d / 28d, 0.2d); |
| checkExactTable(6, 7, 29d / 42d, 0.05d); |
| checkExactTable(4, 10, 7d / 10d, 0.05d); |
| checkExactTable(5, 15, 11d / 15d, 0.02d); |
| checkExactTable(9, 10, 31d / 45d, 0.01d); |
| checkExactTable(7, 10, 43d / 70d, 0.05d); |
| } |
| |
| @Test |
| public void testTwoSampleApproximateCritialValues() { |
| final double tol = .01; |
| final double[] alpha = { |
| 0.10, 0.05, 0.025, 0.01, 0.005, 0.001 |
| }; |
| // From Wikipedia KS article - TODO: get (and test) more precise values |
| final double[] c = { |
| 1.22, 1.36, 1.48, 1.63, 1.73, 1.95 |
| }; |
| final int k[] = { |
| 60, 100, 500 |
| }; |
| double n; |
| double m; |
| for (int i = 0; i < k.length; i++) { |
| for (int j = 0; j < i; j++) { |
| n = k[i]; |
| m = k[j]; |
| for (int l = 0; l < alpha.length; l++) { |
| final double dCrit = c[l] * FastMath.sqrt((n + m) / (n * m)); |
| checkApproximateTable(k[i], k[j], dCrit, alpha[l], tol); |
| } |
| } |
| } |
| } |
| |
| @Test |
| public void testPelzGoodApproximation() { |
| KolmogorovSmirnovTest ksTest = new KolmogorovSmirnovTest(); |
| final double d[] = {0.15, 0.20, 0.25, 0.3, 0.35, 0.4}; |
| final int n[] = {141, 150, 180, 220, 1000}; |
| // Reference values computed using the Pelz method from |
| // http://simul.iro.umontreal.ca/ksdir/KolmogorovSmirnovDist.java |
| final double ref[] = { |
| 0.9968940168727819, 0.9979326624184857, 0.9994677598604506, 0.9999128354780209, 0.9999999999998661, |
| 0.9999797514476236, 0.9999902122242081, 0.9999991327060908, 0.9999999657681911, 0.9999999999977929, |
| 0.9999999706444976, 0.9999999906571532, 0.9999999997949596, 0.999999999998745, 0.9999999999993876, |
| 0.9999999999916627, 0.9999999999984447, 0.9999999999999936, 0.999999999999341, 0.9999999999971508, |
| 0.9999999999999877, 0.9999999999999191, 0.9999999999999254, 0.9999999999998178, 0.9999999999917788, |
| 0.9999999999998556, 0.9999999999992014, 0.9999999999988859, 0.9999999999999325, 0.9999999999821726 |
| }; |
| |
| final double tol = 10e-15; |
| int k = 0; |
| for (int i = 0; i < 6; i++) { |
| for (int j = 0; j < 5; j++, k++) { |
| Assert.assertEquals(ref[k], ksTest.pelzGood(d[i], n[j]), tol); |
| } |
| } |
| } |
| |
| /** Verifies large sample approximate p values against R */ |
| @Test |
| public void testTwoSampleApproximateP() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| // Reference values from R, version 2.15.3 |
| Assert.assertEquals(0.0319983962391632, test.kolmogorovSmirnovTest(gaussian, gaussian2), TOLERANCE); |
| Assert.assertEquals(0.202352941176471, test.kolmogorovSmirnovStatistic(gaussian, gaussian2), TOLERANCE); |
| } |
| |
| /** |
| * MATH-1181 |
| * Verify that large sample method is selected for sample product > Integer.MAX_VALUE |
| * (integer overflow in sample product) |
| */ |
| @Test(timeout=5000) |
| public void testTwoSampleProductSizeOverflow() { |
| final int n = 50000; |
| Assert.assertTrue(n * n < 0); |
| double[] x = new double[n]; |
| double[] y = new double[n]; |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| Assert.assertFalse(Double.isNaN(test.kolmogorovSmirnovTest(x, y))); |
| } |
| |
| /** |
| * Verifies that Monte Carlo simulation gives results close to exact p values. |
| */ |
| @Test |
| public void testTwoSampleMonteCarlo() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(new Well19937c(1000)); |
| final int sampleSize = 14; |
| final double tol = .001; |
| final double[] shortUniform = new double[sampleSize]; |
| System.arraycopy(uniform, 0, shortUniform, 0, sampleSize); |
| final double[] shortGaussian = new double[sampleSize]; |
| final double[] shortGaussian2 = new double[sampleSize]; |
| System.arraycopy(gaussian, 0, shortGaussian, 0, sampleSize); |
| System.arraycopy(gaussian, 10, shortGaussian2, 0, sampleSize); |
| final double[] d = { |
| test.kolmogorovSmirnovStatistic(shortGaussian, shortUniform), |
| test.kolmogorovSmirnovStatistic(shortGaussian2, shortGaussian) |
| }; |
| for (double dv : d) { |
| double exactPStrict = test.exactP(dv, sampleSize, sampleSize, true); |
| double exactPNonStrict = test.exactP(dv, sampleSize, sampleSize, false); |
| double montePStrict = test.monteCarloP(dv, sampleSize, sampleSize, true, |
| KolmogorovSmirnovTest.MONTE_CARLO_ITERATIONS); |
| double montePNonStrict = test.monteCarloP(dv, sampleSize, sampleSize, false, |
| KolmogorovSmirnovTest.MONTE_CARLO_ITERATIONS); |
| Assert.assertEquals(exactPStrict, montePStrict, tol); |
| Assert.assertEquals(exactPNonStrict, montePNonStrict, tol); |
| } |
| } |
| |
| @Test |
| public void testTwoSampleMonteCarloDifferentSampleSizes() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(new Well19937c(1000)); |
| final int sampleSize1 = 14; |
| final int sampleSize2 = 7; |
| final double d = 0.3; |
| final boolean strict = false; |
| final double tol = 1e-2; |
| Assert.assertEquals(test.exactP(d, sampleSize1, sampleSize2, strict), |
| test.monteCarloP(d, sampleSize1, sampleSize2, strict, |
| KolmogorovSmirnovTest.MONTE_CARLO_ITERATIONS), |
| tol); |
| } |
| |
| /** |
| * Performance test for monteCarlo method. Disabled by default. |
| */ |
| // @Test |
| public void testTwoSampleMonteCarloPerformance() { |
| int numIterations = 100000; |
| int N = (int)Math.sqrt(KolmogorovSmirnovTest.LARGE_SAMPLE_PRODUCT); |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(new Well19937c(1000)); |
| for (int n = 2; n <= N; ++n) { |
| long startMillis = System.currentTimeMillis(); |
| int m = KolmogorovSmirnovTest.LARGE_SAMPLE_PRODUCT/n; |
| Assert.assertEquals(0d, test.monteCarloP(Double.POSITIVE_INFINITY, n, m, true, numIterations), 0d); |
| long endMillis = System.currentTimeMillis(); |
| System.out.println("n=" + n + ", m=" + m + ", time=" + (endMillis-startMillis)/1000d + "s"); |
| } |
| } |
| |
| @Test |
| public void testTwoSampleWithManyTies() { |
| // MATH-1197 |
| final double[] x = { |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, |
| 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, |
| 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, |
| 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, |
| 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, |
| 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, |
| 3.181199, 3.181199, 3.181199, 3.181199, 3.181199, 3.181199, |
| 3.723539, 3.723539, 3.723539, 3.723539, 4.383482, 4.383482, |
| 4.383482, 4.383482, 5.320671, 5.320671, 5.320671, 5.717284, |
| 6.964001, 7.352165, 8.710510, 8.710510, 8.710510, 8.710510, |
| 8.710510, 8.710510, 9.539004, 9.539004, 10.720619, 17.726077, |
| 17.726077, 17.726077, 17.726077, 22.053875, 23.799144, 27.355308, |
| 30.584960, 30.584960, 30.584960, 30.584960, 30.751808 |
| }; |
| |
| final double[] y = { |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 2.202653, 2.202653, 2.202653, |
| 2.202653, 2.202653, 2.202653, 2.202653, 2.202653, 3.061758, |
| 3.723539, 5.628420, 5.628420, 5.628420, 5.628420, 5.628420, |
| 6.916982, 6.916982, 6.916982, 10.178538, 10.178538, 10.178538, |
| 10.178538, 10.178538 |
| }; |
| |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| |
| Assert.assertEquals(0.0640394088, test.kolmogorovSmirnovStatistic(x, y), 1e-6); |
| Assert.assertEquals(0.9792777290, test.kolmogorovSmirnovTest(x, y), 1e-6); |
| |
| } |
| |
| @Test |
| public void testTwoSamplesAllEqual() { |
| int iterations = 10000; |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| for (int i = 2; i < 30; ++i) { |
| // testing values with ties |
| double[] values = new double[i]; |
| Arrays.fill(values, i); |
| // testing values without ties |
| double[] ascendingValues = new double[i]; |
| for (int j = 0; j < ascendingValues.length; j++) { |
| ascendingValues[j] = j; |
| } |
| |
| Assert.assertEquals(0., test.kolmogorovSmirnovStatistic(values, values), 0.); |
| Assert.assertEquals(0., test.kolmogorovSmirnovStatistic(ascendingValues, ascendingValues), 0.); |
| |
| if (i < 10) { |
| Assert.assertEquals(1.0, test.exactP(0, values.length, values.length, true), 0.); |
| Assert.assertEquals(1.0, test.exactP(0, values.length, values.length, false), 0.); |
| } |
| |
| Assert.assertEquals(1.0, test.monteCarloP(0, values.length, values.length, true, iterations), 0.); |
| Assert.assertEquals(1.0, test.monteCarloP(0, values.length, values.length, false, iterations), 0.); |
| |
| Assert.assertEquals(1.0, test.approximateP(0, values.length, values.length), 0.); |
| Assert.assertEquals(1.0, test.approximateP(0, values.length, values.length), 0.); |
| } |
| } |
| |
| /** |
| * JIRA: MATH-1245 |
| * |
| * Verify that D-values are not viewed as distinct when they are mathematically equal |
| * when computing p-statistics for small sample tests. Reference values are from R 3.2.0. |
| */ |
| @Test |
| public void testDRounding() { |
| final double tol = 1e-12; |
| final double[] x = {0, 2, 3, 4, 5, 6, 7, 8, 9, 12}; |
| final double[] y = {1, 10, 11, 13, 14, 15, 16, 17, 18}; |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| Assert.assertEquals(0.0027495724090154106, test.kolmogorovSmirnovTest(x, y,false), tol); |
| |
| final double[] x1 = {2, 4, 6, 8, 9, 10, 11, 12, 13}; |
| final double[] y1 = {0, 1, 3, 5, 7}; |
| Assert.assertEquals(0.085914085914085896, test.kolmogorovSmirnovTest(x1, y1, false), tol); |
| |
| final double[] x2 = {4, 6, 7, 8, 9, 10, 11}; |
| final double[] y2 = {0, 1, 2, 3, 5}; |
| Assert.assertEquals(0.015151515151515027, test.kolmogorovSmirnovTest(x2, y2, false), tol); |
| } |
| |
| /** |
| * JIRA: MATH-1245 |
| * |
| * Verify that D-values are not viewed as distinct when they are mathematically equal |
| * when computing p-statistics for small sample tests. Reference values are from R 3.2.0. |
| */ |
| @Test |
| public void testDRoundingMonteCarlo() { |
| final double tol = 1e-2; |
| final int iterations = 1000000; |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(new Well19937c(1000)); |
| |
| final double[] x = {0, 2, 3, 4, 5, 6, 7, 8, 9, 12}; |
| final double[] y = {1, 10, 11, 13, 14, 15, 16, 17, 18}; |
| double d = test.kolmogorovSmirnovStatistic(x, y); |
| Assert.assertEquals(0.0027495724090154106, test.monteCarloP(d, x.length, y.length, false, iterations), tol); |
| |
| final double[] x1 = {2, 4, 6, 8, 9, 10, 11, 12, 13}; |
| final double[] y1 = {0, 1, 3, 5, 7}; |
| d = test.kolmogorovSmirnovStatistic(x1, y1); |
| Assert.assertEquals(0.085914085914085896, test.monteCarloP(d, x1.length, y1.length, false, iterations), tol); |
| |
| final double[] x2 = {4, 6, 7, 8, 9, 10, 11}; |
| final double[] y2 = {0, 1, 2, 3, 5}; |
| d = test.kolmogorovSmirnovStatistic(x2, y2); |
| Assert.assertEquals(0.015151515151515027, test.monteCarloP(d, x2.length, y2.length, false, iterations), tol); |
| } |
| |
| @Test |
| public void testFillBooleanArrayRandomlyWithFixedNumberTrueValues() { |
| |
| final int[][] parameters = {{5, 1}, {5, 2}, {5, 3}, {5, 4}, {8, 1}, {8, 2}, {8, 3}, {8, 4}, {8, 5}, {8, 6}, {8, 7}}; |
| |
| final double alpha = 0.001; |
| final int numIterations = 1000000; |
| |
| final RandomGenerator rng = new Well19937c(0); |
| |
| for (final int[] parameter : parameters) { |
| |
| final int arraySize = parameter[0]; |
| final int numberOfTrueValues = parameter[1]; |
| |
| final boolean[] b = new boolean[arraySize]; |
| final long[] counts = new long[1 << arraySize]; |
| |
| for (int i = 0; i < numIterations; ++i) { |
| KolmogorovSmirnovTest.fillBooleanArrayRandomlyWithFixedNumberTrueValues(b, numberOfTrueValues, rng); |
| int x = 0; |
| for (int j = 0; j < arraySize; ++j) { |
| x = ((x << 1) | ((b[j])?1:0)); |
| } |
| counts[x] += 1; |
| } |
| |
| final int numCombinations = (int) CombinatoricsUtils.binomialCoefficient(arraySize, numberOfTrueValues); |
| |
| final long[] observed = new long[numCombinations]; |
| final double[] expected = new double[numCombinations]; |
| Arrays.fill(expected, numIterations / (double) numCombinations); |
| |
| int observedIdx = 0; |
| |
| for (int i = 0; i < (1 << arraySize); ++i) { |
| if (Integer.bitCount(i) == numberOfTrueValues) { |
| observed[observedIdx] = counts[i]; |
| observedIdx += 1; |
| } |
| else { |
| Assert.assertEquals(0, counts[i]); |
| } |
| } |
| |
| Assert.assertEquals(numCombinations, observedIdx); |
| TestUtils.assertChiSquareAccept(expected, observed, alpha); |
| } |
| } |
| |
| /** |
| * Test an example with ties in the data. Reference data is R 3.2.0, |
| * ks.boot implemented in Matching (Version 4.8-3.4, Build Date: 2013/10/28) |
| */ |
| @Test |
| public void testBootstrapSmallSamplesWithTies() { |
| final double[] x = {0, 2, 4, 6, 8, 8, 10, 15, 22, 30, 33, 36, 38}; |
| final double[] y = {9, 17, 20, 33, 40, 51, 60, 60, 72, 90, 101}; |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(new Well19937c(2000)); |
| Assert.assertEquals(0.0059, test.bootstrap(x, y, 10000, false), 1E-3); |
| } |
| |
| /** |
| * Reference data is R 3.2.0, ks.boot implemented in |
| * Matching (Version 4.8-3.4, Build Date: 2013/10/28) |
| */ |
| @Test |
| public void testBootstrapLargeSamples() { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(new Well19937c(1000)); |
| Assert.assertEquals(0.0237, test.bootstrap(gaussian, gaussian2, 10000), 1E-2); |
| } |
| |
| /** |
| * Test an example where D-values are close (subject to rounding). |
| * Reference data is R 3.2.0, ks.boot implemented in |
| * Matching (Version 4.8-3.4, Build Date: 2013/10/28) |
| */ |
| @Test |
| public void testBootstrapRounding() { |
| final double[] x = {2,4,6,8,9,10,11,12,13}; |
| final double[] y = {0,1,3,5,7}; |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(new Well19937c(1000)); |
| Assert.assertEquals(0.06303, test.bootstrap(x, y, 10000, false), 1E-2); |
| } |
| |
| @Test |
| public void testFixTiesNoOp() throws Exception { |
| final double[] x = {0, 1, 2, 3, 4}; |
| final double[] y = {5, 6, 7, 8}; |
| final double[] origX = MathArrays.copyOf(x); |
| final double[] origY = MathArrays.copyOf(y); |
| fixTies(x,y); |
| Assert.assertArrayEquals(origX, x, 0); |
| Assert.assertArrayEquals(origY, y, 0); |
| } |
| |
| /** |
| * Verify that fixTies is deterministic, i.e, |
| * x = x', y = y' => fixTies(x,y) = fixTies(x', y') |
| */ |
| @Test |
| public void testFixTiesConsistency() throws Exception { |
| final double[] x = {0, 1, 2, 3, 4, 2}; |
| final double[] y = {5, 6, 7, 8, 1, 2}; |
| final double[] xP = MathArrays.copyOf(x); |
| final double[] yP = MathArrays.copyOf(y); |
| checkFixTies(x, y); |
| final double[] fixedX = MathArrays.copyOf(x); |
| final double[] fixedY = MathArrays.copyOf(y); |
| checkFixTies(xP, yP); |
| Assert.assertArrayEquals(fixedX, xP, 0); |
| Assert.assertArrayEquals(fixedY, yP, 0); |
| } |
| |
| @Test |
| public void testFixTies() throws Exception { |
| checkFixTies(new double[] {0, 1, 1, 4, 0}, new double[] {0, 5, 0.5, 0.55, 7}); |
| checkFixTies(new double[] {1, 1, 1, 1, 1}, new double[] {1, 1}); |
| checkFixTies(new double[] {1, 2, 3}, new double[] {1}); |
| checkFixTies(new double[] {1, 1, 0, 1, 0}, new double[] {}); |
| } |
| |
| /** |
| * Checks that fixTies eliminates ties in the data but does not otherwise |
| * perturb the ordering. |
| */ |
| private void checkFixTies(double[] x, double[] y) throws Exception { |
| final double[] origCombined = MathArrays.concatenate(x, y); |
| fixTies(x, y); |
| Assert.assertFalse(hasTies(x, y)); |
| final double[] combined = MathArrays.concatenate(x, y); |
| for (int i = 0; i < combined.length; i++) { |
| for (int j = 0; j < i; j++) { |
| Assert.assertTrue(combined[i] != combined[j]); |
| if (combined[i] < combined[j]) |
| Assert.assertTrue(origCombined[i] < origCombined[j] |
| || origCombined[i] == origCombined[j]); |
| } |
| |
| } |
| } |
| |
| /** |
| * Verifies the inequality exactP(criticalValue, n, m, true) < alpha < exactP(criticalValue, n, |
| * m, false). |
| * |
| * Note that the validity of this check depends on the fact that alpha lies strictly between two |
| * attained values of the distribution and that criticalValue is one of the attained values. The |
| * critical value table (reference below) uses attained values. This test therefore also |
| * verifies that criticalValue is attained. |
| * |
| * @param n first sample size |
| * @param m second sample size |
| * @param criticalValue critical value |
| * @param alpha significance level |
| */ |
| private void checkExactTable(int n, int m, double criticalValue, double alpha) { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| Assert.assertTrue(test.exactP(criticalValue, n, m, true) < alpha); |
| Assert.assertTrue(test.exactP(criticalValue, n, m, false) > alpha); |
| } |
| |
| /** |
| * Verifies that approximateP(criticalValue, n, m) is within epsilon of alpha. |
| * |
| * @param n first sample size |
| * @param m second sample size |
| * @param criticalValue critical value (from table) |
| * @param alpha significance level |
| * @param epsilon tolerance |
| */ |
| private void checkApproximateTable(int n, int m, double criticalValue, double alpha, double epsilon) { |
| final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest(); |
| Assert.assertEquals(alpha, test.approximateP(criticalValue, n, m), epsilon); |
| } |
| |
| /** |
| * Reflection hack to expose private fixTies method for testing. |
| */ |
| private static void fixTies(double[] x, double[] y) throws Exception { |
| Method method = KolmogorovSmirnovTest.class.getDeclaredMethod("fixTies", |
| double[].class, double[].class); |
| method.setAccessible(true); |
| method.invoke(KolmogorovSmirnovTest.class, x, y); |
| } |
| |
| /** |
| * Reflection hack to expose private hasTies method. |
| */ |
| private static boolean hasTies(double[] x, double[] y) throws Exception { |
| Method method = KolmogorovSmirnovTest.class.getDeclaredMethod("hasTies", |
| double[].class, double[].class); |
| method.setAccessible(true); |
| return (Boolean) method.invoke(KolmogorovSmirnovTest.class, x, y); |
| } |
| |
| } |
