src/test/java/org/apache/commons/math3/distribution/BinomialDistributionTest.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.junit.Assert;
import org.junit.Test;

/**
 * Test cases for BinomialDistribution. Extends IntegerDistributionAbstractTest.
 * See class javadoc for IntegerDistributionAbstractTest for details.
 *
 */
public class BinomialDistributionTest extends IntegerDistributionAbstractTest {

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

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

    /** Creates the default discrete distribution instance to use in tests. */
    @Override
    public IntegerDistribution makeDistribution() {
        return new BinomialDistribution(10, 0.70);
    }

    /** Creates the default probability density test input values. */
    @Override
    public int[] makeDensityTestPoints() {
        return new int[] { -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 };
    }

    /**
     * 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, 0.0000059049d, 0.000137781d, 0.0014467005,
            0.009001692, 0.036756909, 0.1029193452, 0.200120949, 0.266827932,
            0.2334744405, 0.121060821, 0.0282475249, 0d };
    }

    /** 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, 5.9049e-06, 0.0001436859, 0.0015903864, 0.0105920784,  0.0473489874,
            0.1502683326, 0.3503892816, 0.6172172136, 0.8506916541, 0.9717524751, 1d, 1d };
    }

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

    /**
     * Creates the default inverse cumulative probability density test expected
     * values
     */
    @Override
    public int[] makeInverseCumulativeTestValues() {
        return new int[] { 0, 2, 3, 4, 5, 5, 10, 10, 10, 9, 9, 10 };
    }

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

    /** Test degenerate case p = 0 */
    @Test
    public void testDegenerate0() {
        BinomialDistribution dist = new BinomialDistribution(5, 0.0d);
        setDistribution(dist);
        setCumulativeTestPoints(new int[] { -1, 0, 1, 5, 10 });
        setCumulativeTestValues(new double[] { 0d, 1d, 1d, 1d, 1d });
        setDensityTestPoints(new int[] { -1, 0, 1, 10, 11 });
        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);
    }

    /** Test degenerate case p = 1 */
    @Test
    public void testDegenerate1() {
        BinomialDistribution dist = new BinomialDistribution(5, 1.0d);
        setDistribution(dist);
        setCumulativeTestPoints(new int[] { -1, 0, 1, 2, 5, 10 });
        setCumulativeTestValues(new double[] { 0d, 0d, 0d, 0d, 1d, 1d });
        setDensityTestPoints(new int[] { -1, 0, 1, 2, 5, 10 });
        setDensityTestValues(new double[] { 0d, 0d, 0d, 0d, 1d, 0d });
        setInverseCumulativeTestPoints(new double[] { 0.1d, 0.5d });
        setInverseCumulativeTestValues(new int[] { 5, 5 });
        verifyDensities();
        verifyCumulativeProbabilities();
        verifyInverseCumulativeProbabilities();
        Assert.assertEquals(dist.getSupportLowerBound(), 5);
        Assert.assertEquals(dist.getSupportUpperBound(), 5);
    }

    /** Test degenerate case n = 0 */
    @Test
    public void testDegenerate2() {
        BinomialDistribution dist = new BinomialDistribution(0, 0.01d);
        setDistribution(dist);
        setCumulativeTestPoints(new int[] { -1, 0, 1, 2, 5, 10 });
        setCumulativeTestValues(new double[] { 0d, 1d, 1d, 1d, 1d, 1d });
        setDensityTestPoints(new int[] { -1, 0, 1, 2, 5, 10 });
        setDensityTestValues(new double[] { 0d, 1d, 0d, 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);
    }

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

        dist = new BinomialDistribution(10, 0.5);
        Assert.assertEquals(dist.getNumericalMean(), 10d * 0.5d, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 10d * 0.5d * 0.5d, tol);

        dist = new BinomialDistribution(30, 0.3);
        Assert.assertEquals(dist.getNumericalMean(), 30d * 0.3d, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 30d * 0.3d * (1d - 0.3d), tol);
    }

    @Test
    public void testMath718() {
        // for large trials the evaluation of ContinuedFraction was inaccurate
        // do a sweep over several large trials to test if the current implementation is
        // numerically stable.

        for (int trials = 500000; trials < 20000000; trials += 100000) {
            BinomialDistribution dist = new BinomialDistribution(trials, 0.5);
            int p = dist.inverseCumulativeProbability(0.5);
            Assert.assertEquals(trials / 2, p);
        }
    }
}