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Java example source code file (GammaDistributionTest.java)

This example Java source code file (GammaDistributionTest.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

bufferedreader, expecting, gammadistribution, half_log_2_pi, inputstream, ioexception, notstrictlypositiveexception, old, override, realdistributionabstracttest, string, stringbuilder, summarystatistics, test

The GammaDistributionTest.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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;

import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.special.Gamma;
import org.apache.commons.math3.stat.descriptive.SummaryStatistics;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test cases for GammaDistribution.
 * Extends ContinuousDistributionAbstractTest.  See class javadoc for
 * ContinuousDistributionAbstractTest for details.
 *
 */
public class GammaDistributionTest extends RealDistributionAbstractTest {

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

    /** Creates the default continuous distribution instance to use in tests. */
    @Override
    public GammaDistribution makeDistribution() {
        return new GammaDistribution(4d, 2d);
    }

    /** Creates the default cumulative probability distribution test input values */
    @Override
    public double[] makeCumulativeTestPoints() {
        // quantiles computed using R version 2.9.2
        return new double[] {0.857104827257, 1.64649737269, 2.17973074725, 2.7326367935, 3.48953912565,
                26.1244815584, 20.0902350297, 17.5345461395, 15.5073130559, 13.3615661365};
    }

    /** Creates the default cumulative probability density test expected values */
    @Override
    public double[] makeCumulativeTestValues() {
        return new double[] {0.001, 0.01, 0.025, 0.05, 0.1, 0.999, 0.990, 0.975, 0.950, 0.900};
    }

    /** Creates the default probability density test expected values */
    @Override
    public double[] makeDensityTestValues() {
        return new double[] {0.00427280075546, 0.0204117166709, 0.0362756163658, 0.0542113174239, 0.0773195272491,
                0.000394468852816, 0.00366559696761, 0.00874649473311, 0.0166712508128, 0.0311798227954};
    }

    // --------------------- Override tolerance  --------------
    @Override
    public void setUp() {
        super.setUp();
        setTolerance(1e-9);
    }

    //---------------------------- Additional test cases -------------------------
    @SuppressWarnings("deprecation")
    @Test
    public void testParameterAccessors() {
        GammaDistribution distribution = (GammaDistribution) getDistribution();
        Assert.assertEquals(4d, distribution.getAlpha(), 0);
        Assert.assertEquals(2d, distribution.getBeta(), 0);
    }

    @Test
    public void testPreconditions() {
        try {
            new GammaDistribution(0, 1);
            Assert.fail("Expecting NotStrictlyPositiveException for alpha = 0");
        } catch (NotStrictlyPositiveException ex) {
            // Expected.
        }
        try {
            new GammaDistribution(1, 0);
            Assert.fail("Expecting NotStrictlyPositiveException for alpha = 0");
        } catch (NotStrictlyPositiveException ex) {
            // Expected.
        }
    }

    @Test
    public void testProbabilities() {
        testProbability(-1.000, 4.0, 2.0, .0000);
        testProbability(15.501, 4.0, 2.0, .9499);
        testProbability(0.504, 4.0, 1.0, .0018);
        testProbability(10.011, 1.0, 2.0, .9933);
        testProbability(5.000, 2.0, 2.0, .7127);
    }

    @Test
    public void testValues() {
        testValue(15.501, 4.0, 2.0, .9499);
        testValue(0.504, 4.0, 1.0, .0018);
        testValue(10.011, 1.0, 2.0, .9933);
        testValue(5.000, 2.0, 2.0, .7127);
    }

    private void testProbability(double x, double a, double b, double expected) {
        GammaDistribution distribution = new GammaDistribution( a, b );
        double actual = distribution.cumulativeProbability(x);
        Assert.assertEquals("probability for " + x, expected, actual, 10e-4);
    }

    private void testValue(double expected, double a, double b, double p) {
        GammaDistribution distribution = new GammaDistribution( a, b );
        double actual = distribution.inverseCumulativeProbability(p);
        Assert.assertEquals("critical value for " + p, expected, actual, 10e-4);
    }

    @Test
    public void testDensity() {
        double[] x = new double[]{-0.1, 1e-6, 0.5, 1, 2, 5};
        // R2.5: print(dgamma(x, shape=1, rate=1), digits=10)
        checkDensity(1, 1, x, new double[]{0.000000000000, 0.999999000001, 0.606530659713, 0.367879441171, 0.135335283237, 0.006737946999});
        // R2.5: print(dgamma(x, shape=2, rate=1), digits=10)
        checkDensity(2, 1, x, new double[]{0.000000000000, 0.000000999999, 0.303265329856, 0.367879441171, 0.270670566473, 0.033689734995});
        // R2.5: print(dgamma(x, shape=4, rate=1), digits=10)
        checkDensity(4, 1, x, new double[]{0.000000000e+00, 1.666665000e-19, 1.263605541e-02, 6.131324020e-02, 1.804470443e-01, 1.403738958e-01});
        // R2.5: print(dgamma(x, shape=4, rate=10), digits=10)
        checkDensity(4, 10, x, new double[]{0.000000000e+00, 1.666650000e-15, 1.403738958e+00, 7.566654960e-02, 2.748204830e-05, 4.018228850e-17});
        // R2.5: print(dgamma(x, shape=.1, rate=10), digits=10)
        checkDensity(0.1, 10, x, new double[]{0.000000000e+00, 3.323953832e+04, 1.663849010e-03, 6.007786726e-06, 1.461647647e-10, 5.996008322e-24});
        // R2.5: print(dgamma(x, shape=.1, rate=20), digits=10)
        checkDensity(0.1, 20, x, new double[]{0.000000000e+00, 3.562489883e+04, 1.201557345e-05, 2.923295295e-10, 3.228910843e-19, 1.239484589e-45});
        // R2.5: print(dgamma(x, shape=.1, rate=4), digits=10)
        checkDensity(0.1, 4, x, new double[]{0.000000000e+00, 3.032938388e+04, 3.049322494e-02, 2.211502311e-03, 2.170613371e-05, 5.846590589e-11});
        // R2.5: print(dgamma(x, shape=.1, rate=1), digits=10)
        checkDensity(0.1, 1, x, new double[]{0.000000000e+00, 2.640334143e+04, 1.189704437e-01, 3.866916944e-02, 7.623306235e-03, 1.663849010e-04});
    }

    private void checkDensity(double alpha, double rate, double[] x, double[] expected) {
        GammaDistribution d = new GammaDistribution(alpha, 1 / rate);
        for (int i = 0; i < x.length; i++) {
            Assert.assertEquals(expected[i], d.density(x[i]), 1e-5);
        }
    }

    @Test
    public void testInverseCumulativeProbabilityExtremes() {
        setInverseCumulativeTestPoints(new double[] {0, 1});
        setInverseCumulativeTestValues(new double[] {0, Double.POSITIVE_INFINITY});
        verifyInverseCumulativeProbabilities();
    }

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

        dist = new GammaDistribution(1, 2);
        Assert.assertEquals(dist.getNumericalMean(), 2, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 4, tol);

        dist = new GammaDistribution(1.1, 4.2);
        Assert.assertEquals(dist.getNumericalMean(), 1.1d * 4.2d, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 1.1d * 4.2d * 4.2d, tol);
    }

    private static final double HALF_LOG_2_PI = 0.5 * FastMath.log(2.0 * FastMath.PI);

    public static double logGamma(double x) {
        /*
         * This is a copy of
         * double Gamma.logGamma(double)
         * prior to MATH-849
         */
        double ret;

        if (Double.isNaN(x) || (x <= 0.0)) {
            ret = Double.NaN;
        } else {
            double sum = Gamma.lanczos(x);
            double tmp = x + Gamma.LANCZOS_G + .5;
            ret = ((x + .5) * FastMath.log(tmp)) - tmp +
                HALF_LOG_2_PI + FastMath.log(sum / x);
        }

        return ret;
    }

    public static double density(final double x, final double shape,
                                 final double scale) {
        /*
         * This is a copy of
         * double GammaDistribution.density(double)
         * prior to MATH-753.
         */
        if (x < 0) {
            return 0;
        }
        return FastMath.pow(x / scale, shape - 1) / scale *
               FastMath.exp(-x / scale) / FastMath.exp(logGamma(shape));
    }

    /*
     * MATH-753: large values of x or shape parameter cause density(double) to
     * overflow. Reference data is generated with the Maxima script
     * gamma-distribution.mac, which can be found in
     * src/test/resources/org/apache/commons/math3/distribution.
     */

    private void doTestMath753(final double shape,
        final double meanNoOF, final double sdNoOF,
        final double meanOF, final double sdOF,
        final String resourceName) throws IOException {
        final GammaDistribution distribution = new GammaDistribution(shape, 1.0);
        final SummaryStatistics statOld = new SummaryStatistics();
        final SummaryStatistics statNewNoOF = new SummaryStatistics();
        final SummaryStatistics statNewOF = new SummaryStatistics();

        final InputStream resourceAsStream;
        resourceAsStream = this.getClass().getResourceAsStream(resourceName);
        Assert.assertNotNull("Could not find resource " + resourceName,
                             resourceAsStream);
        final BufferedReader in;
        in = new BufferedReader(new InputStreamReader(resourceAsStream));

        try {
            for (String line = in.readLine(); line != null; line = in.readLine()) {
                if (line.startsWith("#")) {
                    continue;
                }
                final String[] tokens = line.split(", ");
                Assert.assertTrue("expected two floating-point values",
                                  tokens.length == 2);
                final double x = Double.parseDouble(tokens[0]);
                final String msg = "x = " + x + ", shape = " + shape +
                                   ", scale = 1.0";
                final double expected = Double.parseDouble(tokens[1]);
                final double ulp = FastMath.ulp(expected);
                final double actualOld = density(x, shape, 1.0);
                final double actualNew = distribution.density(x);
                final double errOld, errNew;
                errOld = FastMath.abs((actualOld - expected) / ulp);
                errNew = FastMath.abs((actualNew - expected) / ulp);

                if (Double.isNaN(actualOld) || Double.isInfinite(actualOld)) {
                    Assert.assertFalse(msg, Double.isNaN(actualNew));
                    Assert.assertFalse(msg, Double.isInfinite(actualNew));
                    statNewOF.addValue(errNew);
                } else {
                    statOld.addValue(errOld);
                    statNewNoOF.addValue(errNew);
                }
            }
            if (statOld.getN() != 0) {
                /*
                 * If no overflow occurs, check that new implementation is
                 * better than old one.
                 */
                final StringBuilder sb = new StringBuilder("shape = ");
                sb.append(shape);
                sb.append(", scale = 1.0\n");
                sb.append("Old implementation\n");
                sb.append("------------------\n");
                sb.append(statOld.toString());
                sb.append("New implementation\n");
                sb.append("------------------\n");
                sb.append(statNewNoOF.toString());
                final String msg = sb.toString();

                final double oldMin = statOld.getMin();
                final double newMin = statNewNoOF.getMin();
                Assert.assertTrue(msg, newMin <= oldMin);

                final double oldMax = statOld.getMax();
                final double newMax = statNewNoOF.getMax();
                Assert.assertTrue(msg, newMax <= oldMax);

                final double oldMean = statOld.getMean();
                final double newMean = statNewNoOF.getMean();
                Assert.assertTrue(msg, newMean <= oldMean);

                final double oldSd = statOld.getStandardDeviation();
                final double newSd = statNewNoOF.getStandardDeviation();
                Assert.assertTrue(msg, newSd <= oldSd);

                Assert.assertTrue(msg, newMean <= meanNoOF);
                Assert.assertTrue(msg, newSd <= sdNoOF);
            }
            if (statNewOF.getN() != 0) {
                final double newMean = statNewOF.getMean();
                final double newSd = statNewOF.getStandardDeviation();

                final StringBuilder sb = new StringBuilder("shape = ");
                sb.append(shape);
                sb.append(", scale = 1.0");
                sb.append(", max. mean error (ulps) = ");
                sb.append(meanOF);
                sb.append(", actual mean error (ulps) = ");
                sb.append(newMean);
                sb.append(", max. sd of error (ulps) = ");
                sb.append(sdOF);
                sb.append(", actual sd of error (ulps) = ");
                sb.append(newSd);
                final String msg = sb.toString();

                Assert.assertTrue(msg, newMean <= meanOF);
                Assert.assertTrue(msg, newSd <= sdOF);
            }
        } catch (IOException e) {
            Assert.fail(e.getMessage());
        } finally {
            in.close();
        }
    }


    @Test
    public void testMath753Shape1() throws IOException {
        doTestMath753(1.0, 1.5, 0.5, 0.0, 0.0, "gamma-distribution-shape-1.csv");
    }

    @Test
    public void testMath753Shape8() throws IOException {
        doTestMath753(8.0, 1.5, 1.0, 0.0, 0.0, "gamma-distribution-shape-8.csv");
    }

    @Test
    public void testMath753Shape10() throws IOException {
        doTestMath753(10.0, 1.0, 1.0, 0.0, 0.0, "gamma-distribution-shape-10.csv");
    }

    @Test
    public void testMath753Shape100() throws IOException {
        doTestMath753(100.0, 1.5, 1.0, 0.0, 0.0, "gamma-distribution-shape-100.csv");
    }

    @Test
    public void testMath753Shape142() throws IOException {
        doTestMath753(142.0, 3.3, 1.6, 40.0, 40.0, "gamma-distribution-shape-142.csv");
    }

    @Test
    public void testMath753Shape1000() throws IOException {
        doTestMath753(1000.0, 1.0, 1.0, 160.0, 220.0, "gamma-distribution-shape-1000.csv");
    }
}

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