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Java example source code file (PoissonDistributionTest.java)

This example Java source code file (PoissonDistributionTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

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Java - Java tags/keywords

default_test_poisson_parameter, exception, extended, integerdistribution, integerdistributionabstracttest, nan, override, poissondistribution, poissondistributiontest, reduced, test, zero

The PoissonDistributionTest.java Java example source code

/*
 * 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.util.FastMath;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.junit.Assert;
import org.junit.Test;

/**
 * <code>PoissonDistributionTest
 *
 */
public class PoissonDistributionTest extends IntegerDistributionAbstractTest {

    /**
     * Poisson parameter value for the test distribution.
     */
    private static final double DEFAULT_TEST_POISSON_PARAMETER = 4.0;

    /**
     * Constructor.
     */
    public PoissonDistributionTest() {
        setTolerance(1e-12);
    }

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

    /**
     * Creates the default probability density test input values.
     */
    @Override
    public int[] makeDensityTestPoints() {
        return new int[] { -1, 0, 1, 2, 3, 4, 5, 10, 20};
    }

    /**
     * Creates the default probability density test expected values.
     * These and all other test values are generated by R, version 1.8.1
     */
    @Override
    public double[] makeDensityTestValues() {
        return new double[] { 0d, 0.0183156388887d,  0.073262555555d,
                0.14652511111d, 0.195366814813d, 0.195366814813,
                0.156293451851d, 0.00529247667642d, 8.27746364655e-09};
    }

    /**
     * Creates the default logarithmic probability density test expected values.
     * Reference values are from R, version 2.14.1.
     */
    @Override
    public double[] makeLogDensityTestValues() {
        return new double[] { Double.NEGATIVE_INFINITY, -4.000000000000d,
                -2.613705638880d, -1.920558458320d, -1.632876385868d,
                -1.632876385868d, -1.856019937183d, -5.241468961877d,
                -18.609729238356d};
    }

    /**
     * Creates the default cumulative probability density test input values.
     */
    @Override
    public int[] makeCumulativeTestPoints() {
        return new int[] { -1, 0, 1, 2, 3, 4, 5, 10, 20 };
    }

    /**
     * Creates the default cumulative probability density test expected values.
     */
    @Override
    public double[] makeCumulativeTestValues() {
        return new double[] { 0d,  0.0183156388887d, 0.0915781944437d,
                0.238103305554d, 0.433470120367d, 0.62883693518,
                0.78513038703d,  0.99716023388d, 0.999999998077 };
    }

    /**
     * Creates the default inverse cumulative probability test input values.
     */
    @Override
    public double[] makeInverseCumulativeTestPoints() {
        IntegerDistribution dist = getDistribution();
        return new double[] { 0d, 0.018315638886d, 0.018315638890d,
                0.091578194441d, 0.091578194445d, 0.238103305552d,
                0.238103305556d, dist.cumulativeProbability(3),
                dist.cumulativeProbability(4), dist.cumulativeProbability(5),
                dist.cumulativeProbability(10), dist.cumulativeProbability(20)};
    }

    /**
     * Creates the default inverse cumulative probability density test expected values.
     */
    @Override
    public int[] makeInverseCumulativeTestValues() {
        return new int[] { 0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 10, 20};
    }

    /**
     * Test the normal approximation of the Poisson distribution by
     * calculating P(90 ≤ X ≤ 110) for X = Po(100) and
     * P(9900 ≤ X ≤ 10200) for X  = Po(10000)
     */
    @Test
    public void testNormalApproximateProbability() {
        PoissonDistribution dist = new PoissonDistribution(100);
        double result = dist.normalApproximateProbability(110)
                - dist.normalApproximateProbability(89);
        Assert.assertEquals(0.706281887248, result, 1E-10);

        dist = new PoissonDistribution(10000);
        result = dist.normalApproximateProbability(10200)
        - dist.normalApproximateProbability(9899);
        Assert.assertEquals(0.820070051552, result, 1E-10);
    }

    /**
     * Test the degenerate cases of a 0.0 and 1.0 inverse cumulative probability.
     */
    @Test
    public void testDegenerateInverseCumulativeProbability() {
        PoissonDistribution dist = new PoissonDistribution(DEFAULT_TEST_POISSON_PARAMETER);
        Assert.assertEquals(Integer.MAX_VALUE, dist.inverseCumulativeProbability(1.0d));
        Assert.assertEquals(0, dist.inverseCumulativeProbability(0d));
    }

    @Test(expected=NotStrictlyPositiveException.class)
    public void testNegativeMean() {
        new PoissonDistribution(-1);
    }

    @Test
    public void testMean() {
        PoissonDistribution dist = new PoissonDistribution(10.0);
        Assert.assertEquals(10.0, dist.getMean(), 0.0);
    }

    @Test
    public void testLargeMeanCumulativeProbability() {
        double mean = 1.0;
        while (mean <= 10000000.0) {
            PoissonDistribution dist = new PoissonDistribution(mean);

            double x = mean * 2.0;
            double dx = x / 10.0;
            double p = Double.NaN;
            double sigma = FastMath.sqrt(mean);
            while (x >= 0) {
                try {
                    p = dist.cumulativeProbability((int) x);
                    Assert.assertFalse("NaN cumulative probability returned for mean = " +
                            mean + " x = " + x,Double.isNaN(p));
                    if (x > mean - 2 * sigma) {
                        Assert.assertTrue("Zero cum probaility returned for mean = " +
                                mean + " x = " + x, p > 0);
                    }
                } catch (Exception ex) {
                    Assert.fail("mean of " + mean + " and x of " + x + " caused " + ex.getMessage());
                }
                x -= dx;
            }

            mean *= 10.0;
        }
    }

    /**
     * JIRA: MATH-282
     */
    @Test
    public void testCumulativeProbabilitySpecial() {
        PoissonDistribution dist;
        dist = new PoissonDistribution(9120);
        checkProbability(dist, 9075);
        checkProbability(dist, 9102);
        dist = new PoissonDistribution(5058);
        checkProbability(dist, 5044);
        dist = new PoissonDistribution(6986);
        checkProbability(dist, 6950);
    }

    private void checkProbability(PoissonDistribution dist, int x) {
        double p = dist.cumulativeProbability(x);
        Assert.assertFalse("NaN cumulative probability returned for mean = " +
                dist.getMean() + " x = " + x, Double.isNaN(p));
        Assert.assertTrue("Zero cum probability returned for mean = " +
                dist.getMean() + " x = " + x, p > 0);
    }

    @Test
    public void testLargeMeanInverseCumulativeProbability() {
        double mean = 1.0;
        while (mean <= 100000.0) { // Extended test value: 1E7.  Reduced to limit run time.
            PoissonDistribution dist = new PoissonDistribution(mean);
            double p = 0.1;
            double dp = p;
            while (p < .99) {
                try {
                    int ret = dist.inverseCumulativeProbability(p);
                    // Verify that returned value satisties definition
                    Assert.assertTrue(p <= dist.cumulativeProbability(ret));
                    Assert.assertTrue(p > dist.cumulativeProbability(ret - 1));
                } catch (Exception ex) {
                    Assert.fail("mean of " + mean + " and p of " + p + " caused " + ex.getMessage());
                }
                p += dp;
            }
            mean *= 10.0;
        }
    }

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

        dist = new PoissonDistribution(1);
        Assert.assertEquals(dist.getNumericalMean(), 1, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 1, tol);

        dist = new PoissonDistribution(11.23);
        Assert.assertEquals(dist.getNumericalMean(), 11.23, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 11.23, tol);
    }
}

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