src/test/java/org/apache/commons/math3/distribution/HypergeometricDistributionTest.java

/*
 * 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.distribution;

import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.util.Precision;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test cases for HyperGeometriclDistribution.
 * Extends IntegerDistributionAbstractTest.  See class javadoc for
 * IntegerDistributionAbstractTest for details.
 *
 */
public class HypergeometricDistributionTest extends IntegerDistributionAbstractTest {

    /**
     * Constructor to override default tolerance.
     */
    public HypergeometricDistributionTest() {
        setTolerance(1e-12);
    }

    //-------------- Implementations for abstract methods -----------------------

    /** Creates the default discrete distribution instance to use in tests. */
    @Override
    public IntegerDistribution makeDistribution() {
        return new HypergeometricDistribution(10, 5, 5);
    }

    /** Creates the default probability density test input values */
    @Override
    public int[] makeDensityTestPoints() {
        return new int[] {-1, 0, 1, 2, 3, 4, 5, 10};
    }

    /**
     * Creates the default probability density test expected values
     * Reference values are from R, version 2.15.3.
     */
    @Override
    public double[] makeDensityTestValues() {
        return new double[] {0d, 0.00396825396825, 0.0992063492063, 0.396825396825, 0.396825396825,
            0.0992063492063, 0.00396825396825, 0d};
    }

    /**
     * Creates the default probability log density test expected values
     * Reference values are from R, version 2.14.1.
     */
    @Override
    public double[] makeLogDensityTestValues() {
        //-Inf  -Inf
        return new double[] {Double.NEGATIVE_INFINITY, -5.52942908751142, -2.31055326264322, -0.924258901523332,
                -0.924258901523332, -2.31055326264322, -5.52942908751142, Double.NEGATIVE_INFINITY};
    }

    /** Creates the default cumulative probability density test input values */
    @Override
    public int[] makeCumulativeTestPoints() {
        return makeDensityTestPoints();
    }

    /**
     * Creates the default cumulative probability density test expected values
     * Reference values are from R, version 2.15.3.
     */
    @Override
    public double[] makeCumulativeTestValues() {
        return new double[] {0d, 0.00396825396825, 0.103174603175, .5, 0.896825396825, 0.996031746032,
                1, 1};
    }

    /** Creates the default inverse cumulative probability test input values */
    @Override
    public double[] makeInverseCumulativeTestPoints() {
        return new double[] {0d, 0.001d, 0.010d, 0.025d, 0.050d, 0.100d, 0.999d,
                0.990d, 0.975d, 0.950d, 0.900d, 1d};
    }

    /** Creates the default inverse cumulative probability density test expected values */
    @Override
    public int[] makeInverseCumulativeTestValues() {
        return new int[] {0, 0, 1, 1, 1, 1, 5, 4, 4, 4, 4, 5};
    }

    //-------------------- Additional test cases ------------------------------

    /** Verify that if there are no failures, mass is concentrated on sampleSize */
    @Test
    public void testDegenerateNoFailures() {
        HypergeometricDistribution dist = new HypergeometricDistribution(5,5,3);
        setDistribution(dist);
        setCumulativeTestPoints(new int[] {-1, 0, 1, 3, 10 });
        setCumulativeTestValues(new double[] {0d, 0d, 0d, 1d, 1d});
        setDensityTestPoints(new int[] {-1, 0, 1, 3, 10});
        setDensityTestValues(new double[] {0d, 0d, 0d, 1d, 0d});
        setInverseCumulativeTestPoints(new double[] {0.1d, 0.5d});
        setInverseCumulativeTestValues(new int[] {3, 3});
        verifyDensities();
        verifyCumulativeProbabilities();
        verifyInverseCumulativeProbabilities();
        Assert.assertEquals(dist.getSupportLowerBound(), 3);
        Assert.assertEquals(dist.getSupportUpperBound(), 3);
    }

    /** Verify that if there are no successes, mass is concentrated on 0 */
    @Test
    public void testDegenerateNoSuccesses() {
        HypergeometricDistribution dist = new HypergeometricDistribution(5,0,3);
        setDistribution(dist);
        setCumulativeTestPoints(new int[] {-1, 0, 1, 3, 10 });
        setCumulativeTestValues(new double[] {0d, 1d, 1d, 1d, 1d});
        setDensityTestPoints(new int[] {-1, 0, 1, 3, 10});
        setDensityTestValues(new double[] {0d, 1d, 0d, 0d, 0d});
        setInverseCumulativeTestPoints(new double[] {0.1d, 0.5d});
        setInverseCumulativeTestValues(new int[] {0, 0});
        verifyDensities();
        verifyCumulativeProbabilities();
        verifyInverseCumulativeProbabilities();
        Assert.assertEquals(dist.getSupportLowerBound(), 0);
        Assert.assertEquals(dist.getSupportUpperBound(), 0);
    }

    /** Verify that if sampleSize = populationSize, mass is concentrated on numberOfSuccesses */
    @Test
    public void testDegenerateFullSample() {
        HypergeometricDistribution dist = new HypergeometricDistribution(5,3,5);
        setDistribution(dist);
        setCumulativeTestPoints(new int[] {-1, 0, 1, 3, 10 });
        setCumulativeTestValues(new double[] {0d, 0d, 0d, 1d, 1d});
        setDensityTestPoints(new int[] {-1, 0, 1, 3, 10});
        setDensityTestValues(new double[] {0d, 0d, 0d, 1d, 0d});
        setInverseCumulativeTestPoints(new double[] {0.1d, 0.5d});
        setInverseCumulativeTestValues(new int[] {3, 3});
        verifyDensities();
        verifyCumulativeProbabilities();
        verifyInverseCumulativeProbabilities();
        Assert.assertEquals(dist.getSupportLowerBound(), 3);
        Assert.assertEquals(dist.getSupportUpperBound(), 3);
    }

    @Test
    public void testPreconditions() {
        try {
            new HypergeometricDistribution(0, 3, 5);
            Assert.fail("negative population size. NotStrictlyPositiveException expected");
        } catch(NotStrictlyPositiveException ex) {
            // Expected.
        }
        try {
            new HypergeometricDistribution(5, -1, 5);
            Assert.fail("negative number of successes. NotPositiveException expected");
        } catch(NotPositiveException ex) {
            // Expected.
        }
        try {
            new HypergeometricDistribution(5, 3, -1);
            Assert.fail("negative sample size. NotPositiveException expected");
        } catch(NotPositiveException ex) {
            // Expected.
        }
        try {
            new HypergeometricDistribution(5, 6, 5);
            Assert.fail("numberOfSuccesses > populationSize. NumberIsTooLargeException expected");
        } catch(NumberIsTooLargeException ex) {
            // Expected.
        }
        try {
            new HypergeometricDistribution(5, 3, 6);
            Assert.fail("sampleSize > populationSize. NumberIsTooLargeException expected");
        } catch(NumberIsTooLargeException ex) {
            // Expected.
        }
    }

    @Test
    public void testAccessors() {
        HypergeometricDistribution dist = new HypergeometricDistribution(5, 3, 4);
        Assert.assertEquals(5, dist.getPopulationSize());
        Assert.assertEquals(3, dist.getNumberOfSuccesses());
        Assert.assertEquals(4, dist.getSampleSize());
    }

    @Test
    public void testLargeValues() {
        int populationSize = 3456;
        int sampleSize = 789;
        int numberOfSucceses = 101;
        double[][] data = {
            {0.0, 2.75646034603961e-12, 2.75646034603961e-12, 1.0},
            {1.0, 8.55705370142386e-11, 8.83269973602783e-11, 0.999999999997244},
            {2.0, 1.31288129219665e-9, 1.40120828955693e-9, 0.999999999911673},
            {3.0, 1.32724172984193e-8, 1.46736255879763e-8, 0.999999998598792},
            {4.0, 9.94501711734089e-8, 1.14123796761385e-7, 0.999999985326375},
            {5.0, 5.89080768883643e-7, 7.03204565645028e-7, 0.999999885876203},
            {20.0, 0.0760051397707708, 0.27349758476299, 0.802507555007781},
            {21.0, 0.087144222047629, 0.360641806810619, 0.72650241523701},
            {22.0, 0.0940378846881819, 0.454679691498801, 0.639358193189381},
            {23.0, 0.0956897500614809, 0.550369441560282, 0.545320308501199},
            {24.0, 0.0919766921922999, 0.642346133752582, 0.449630558439718},
            {25.0, 0.083641637261095, 0.725987771013677, 0.357653866247418},
            {96.0, 5.93849188852098e-57, 1.0, 6.01900244560712e-57},
            {97.0, 7.96593036832547e-59, 1.0, 8.05105570861321e-59},
            {98.0, 8.44582921934367e-61, 1.0, 8.5125340287733e-61},
            {99.0, 6.63604297068222e-63, 1.0, 6.670480942963e-63},
            {100.0, 3.43501099007557e-65, 1.0, 3.4437972280786e-65},
            {101.0, 8.78623800302957e-68, 1.0, 8.78623800302957e-68},
        };

        testHypergeometricDistributionProbabilities(populationSize, sampleSize, numberOfSucceses, data);
    }

    private void testHypergeometricDistributionProbabilities(int populationSize, int sampleSize, int numberOfSucceses, double[][] data) {
        HypergeometricDistribution dist = new HypergeometricDistribution(populationSize, numberOfSucceses, sampleSize);
        for (int i = 0; i < data.length; ++i) {
            int x = (int)data[i][0];
            double pmf = data[i][1];
            double actualPmf = dist.probability(x);
            TestUtils.assertRelativelyEquals("Expected equals for <"+x+"> pmf",pmf, actualPmf, 1.0e-9);

            double cdf = data[i][2];
            double actualCdf = dist.cumulativeProbability(x);
            TestUtils.assertRelativelyEquals("Expected equals for <"+x+"> cdf",cdf, actualCdf, 1.0e-9);

            double cdf1 = data[i][3];
            double actualCdf1 = dist.upperCumulativeProbability(x);
            TestUtils.assertRelativelyEquals("Expected equals for <"+x+"> cdf1",cdf1, actualCdf1, 1.0e-9);
        }
    }

    @Test
    public void testMoreLargeValues() {
        int populationSize = 26896;
        int sampleSize = 895;
        int numberOfSucceses = 55;
        double[][] data = {
            {0.0, 0.155168304750504, 0.155168304750504, 1.0},
            {1.0, 0.29437545000746, 0.449543754757964, 0.844831695249496},
            {2.0, 0.273841321577003, 0.723385076334967, 0.550456245242036},
            {3.0, 0.166488572570786, 0.889873648905753, 0.276614923665033},
            {4.0, 0.0743969744713231, 0.964270623377076, 0.110126351094247},
            {5.0, 0.0260542785784855, 0.990324901955562, 0.0357293766229237},
            {20.0, 3.57101101678792e-16, 1.0, 3.78252101622096e-16},
            {21.0, 2.00551638598312e-17, 1.0, 2.11509999433041e-17},
            {22.0, 1.04317070180562e-18, 1.0, 1.09583608347287e-18},
            {23.0, 5.03153504903308e-20, 1.0, 5.266538166725e-20},
            {24.0, 2.2525984149695e-21, 1.0, 2.35003117691919e-21},
            {25.0, 9.3677424515947e-23, 1.0, 9.74327619496943e-23},
            {50.0, 9.83633962945521e-69, 1.0, 9.8677629437617e-69},
            {51.0, 3.13448949497553e-71, 1.0, 3.14233143064882e-71},
            {52.0, 7.82755221928122e-74, 1.0, 7.84193567329055e-74},
            {53.0, 1.43662126065532e-76, 1.0, 1.43834540093295e-76},
            {54.0, 1.72312692517348e-79, 1.0, 1.7241402776278e-79},
            {55.0, 1.01335245432581e-82, 1.0, 1.01335245432581e-82},
        };
        testHypergeometricDistributionProbabilities(populationSize, sampleSize, numberOfSucceses, data);
    }

    @Test
    public void testMoments() {
        final double tol = 1e-9;
        HypergeometricDistribution dist;

        dist = new HypergeometricDistribution(1500, 40, 100);
        Assert.assertEquals(dist.getNumericalMean(), 40d * 100d / 1500d, tol);
        Assert.assertEquals(dist.getNumericalVariance(), ( 100d * 40d * (1500d - 100d) * (1500d - 40d) ) / ( (1500d * 1500d * 1499d) ), tol);

        dist = new HypergeometricDistribution(3000, 55, 200);
        Assert.assertEquals(dist.getNumericalMean(), 55d * 200d / 3000d, tol);
        Assert.assertEquals(dist.getNumericalVariance(), ( 200d * 55d * (3000d - 200d) * (3000d - 55d) ) / ( (3000d * 3000d * 2999d) ), tol);
    }

    @Test
    public void testMath644() {
        int N = 14761461;  // population
        int m = 1035;      // successes in population
        int n = 1841;      // number of trials

        int k = 0;
        final HypergeometricDistribution dist = new HypergeometricDistribution(N, m, n);

        Assert.assertTrue(Precision.compareTo(1.0, dist.upperCumulativeProbability(k), 1) == 0);
        Assert.assertTrue(Precision.compareTo(dist.cumulativeProbability(k), 0.0, 1) > 0);

        // another way to calculate the upper cumulative probability
        double upper = 1.0 - dist.cumulativeProbability(k) + dist.probability(k);
        Assert.assertTrue(Precision.compareTo(1.0, upper, 1) == 0);
    }

    @Test
    public void testMath1021() {
        final int N = 43130568;
        final int m = 42976365;
        final int n = 50;
        final HypergeometricDistribution dist = new HypergeometricDistribution(N, m, n);

        for (int i = 0; i < 100; i++) {
            final int sample = dist.sample();
            Assert.assertTrue("sample=" + sample, 0 <= sample);
            Assert.assertTrue("sample=" + sample, sample <= n);
        }
    }
}