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Java example source code file (ParetoDistributionTest.java)

This example Java source code file (ParetoDistributionTest.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

override, paretodistribution, paretodistributiontest, realdistributionabstracttest, test

The ParetoDistributionTest.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.exception.NotStrictlyPositiveException;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test cases for {@link ParetoDistribution}.
 * <p>
 * Extends {@link RealDistributionAbstractTest}. See class javadoc of that class for details.
 *
 * @since 3.3
 */
public class ParetoDistributionTest extends RealDistributionAbstractTest {

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

    /** Creates the default real distribution instance to use in tests. */
    @Override
    public ParetoDistribution makeDistribution() {
        return new ParetoDistribution(2.1, 1.4);
    }

    /** Creates the default cumulative probability distribution test input values */
    @Override
    public double[] makeCumulativeTestPoints() {
        // quantiles computed using R
        return new double[] { -2.226325228634938, -1.156887023657177, -0.643949578356075, -0.2027950777320613, 0.305827808237559,
                              +6.42632522863494, 5.35688702365718, 4.843949578356074, 4.40279507773206, 3.89417219176244 };
    }

    /** Creates the default cumulative probability density test expected values */
    @Override
    public double[] makeCumulativeTestValues() {
        return new double[] { 0, 0, 0, 0, 0, 0.791089998892, 0.730456085931, 0.689667290488, 0.645278794701, 0.578763688757 };
    }

    /** Creates the default probability density test expected values */
    @Override
    public double[] makeDensityTestValues() {
        return new double[] { 0, 0, 0, 0, 0, 0.0455118580441, 0.070444173646, 0.0896924681582, 0.112794186114, 0.151439332084 };
    }

    /**
     * Creates the default inverse cumulative probability distribution test input values.
     */
    @Override
    public double[] makeInverseCumulativeTestPoints() {
        // Exclude the test points less than zero, as they have cumulative
        // probability of zero, meaning the inverse returns zero, and not the
        // points less than zero.
        double[] points = makeCumulativeTestValues();
        double[] points2 = new double[points.length - 5];
        System.arraycopy(points, 5, points2, 0, points.length - 5);
        return points2;
    }

    /**
     * Creates the default inverse cumulative probability test expected values.
     */
    @Override
    public double[] makeInverseCumulativeTestValues() {
        // Exclude the test points less than zero, as they have cumulative
        // probability of zero, meaning the inverse returns zero, and not the
        // points less than zero.
        double[] points = makeCumulativeTestPoints();
        double[] points2 = new double[points.length - 5];
        System.arraycopy(points, 5, points2, 0, points.length - 5);
        return points2;
    }

    // --------------------- Override tolerance  --------------
    @Override
    public void setUp() {
        super.setUp();
        setTolerance(ParetoDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    }

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

    private void verifyQuantiles() {
        ParetoDistribution distribution = (ParetoDistribution)getDistribution();
        double mu = distribution.getScale();
        double sigma = distribution.getShape();
        setCumulativeTestPoints( new double[] { mu - 2 *sigma,  mu - sigma,
                                                mu,             mu + sigma,
                                                mu + 2 * sigma, mu + 3 * sigma,
                                                mu + 4 * sigma, mu + 5 * sigma });
        verifyCumulativeProbabilities();
    }

    @Test
    public void testQuantiles() {
        setCumulativeTestValues(new double[] {0, 0, 0, 0.510884134236, 0.694625688662, 0.785201995008, 0.837811522357, 0.871634279326});
        setDensityTestValues(new double[] {0, 0, 0.666666666, 0.195646346305, 0.0872498032394, 0.0477328899983, 0.0294888141169, 0.0197485724114});
        verifyQuantiles();
        verifyDensities();

        setDistribution(new ParetoDistribution(1, 1));
        setCumulativeTestValues(new double[] {0, 0, 0, 0.5, 0.666666666667, 0.75, 0.8, 0.833333333333});
        setDensityTestValues(new double[] {0, 0, 1.0, 0.25, 0.111111111111, 0.0625, 0.04, 0.0277777777778});
        verifyQuantiles();
        verifyDensities();

        setDistribution(new ParetoDistribution(0.1, 0.1));
        setCumulativeTestValues(new double[] {0, 0, 0, 0.0669670084632, 0.104041540159, 0.129449436704, 0.148660077479, 0.164041197922});
        setDensityTestValues(new double[] {0, 0, 1.0, 0.466516495768, 0.298652819947, 0.217637640824, 0.170267984504, 0.139326467013});
        verifyQuantiles();
        verifyDensities();
    }

    @Test
    public void testInverseCumulativeProbabilityExtremes() {
        setInverseCumulativeTestPoints(new double[] {0, 1});
        setInverseCumulativeTestValues(new double[] {2.1, Double.POSITIVE_INFINITY});
        verifyInverseCumulativeProbabilities();
    }

    @Test
    public void testGetScale() {
        ParetoDistribution distribution = (ParetoDistribution)getDistribution();
        Assert.assertEquals(2.1, distribution.getScale(), 0);
    }

    @Test
    public void testGetShape() {
        ParetoDistribution distribution = (ParetoDistribution)getDistribution();
        Assert.assertEquals(1.4, distribution.getShape(), 0);
    }

    @Test(expected=NotStrictlyPositiveException.class)
    public void testPreconditions() {
        new ParetoDistribution(1, 0);
    }

    @Test
    public void testDensity() {
        double [] x = new double[]{-2, -1, 0, 1, 2};
        // R 2.14: print(dpareto(c(-2,-1,0,1,2), scale=1, shape=1), digits=10)
        checkDensity(1, 1, x, new double[] { 0.00, 0.00, 0.00, 1.00, 0.25 });
        // R 2.14: print(dpareto(c(-2,-1,0,1,2), scale=1.1, shape=1), digits=10)
        checkDensity(1.1, 1, x, new double[] { 0.000, 0.000, 0.000, 0.000, 0.275 });
    }

    private void checkDensity(double scale, double shape, double[] x,
        double[] expected) {
        ParetoDistribution d = new ParetoDistribution(scale, shape);
        for (int i = 0; i < x.length; i++) {
            Assert.assertEquals(expected[i], d.density(x[i]), 1e-9);
        }
    }

    /**
     * Check to make sure top-coding of extreme values works correctly.
     */
    @Test
    public void testExtremeValues() {
        ParetoDistribution d = new ParetoDistribution(1, 1);
        for (int i = 0; i < 1e5; i++) { // make sure no convergence exception
            double upperTail = d.cumulativeProbability(i);
            if (i <= 1000) { // make sure not top-coded
                Assert.assertTrue(upperTail < 1.0d);
            }
            else { // make sure top coding not reversed
                Assert.assertTrue(upperTail > 0.999);
            }
        }

        Assert.assertEquals(d.cumulativeProbability(Double.MAX_VALUE), 1, 0);
        Assert.assertEquals(d.cumulativeProbability(-Double.MAX_VALUE), 0, 0);
        Assert.assertEquals(d.cumulativeProbability(Double.POSITIVE_INFINITY), 1, 0);
        Assert.assertEquals(d.cumulativeProbability(Double.NEGATIVE_INFINITY), 0, 0);
    }

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

        dist = new ParetoDistribution(1, 1);
        Assert.assertEquals(dist.getNumericalMean(), Double.POSITIVE_INFINITY, tol);
        Assert.assertEquals(dist.getNumericalVariance(), Double.POSITIVE_INFINITY, tol);

        dist = new ParetoDistribution(2.2, 2.4);
        Assert.assertEquals(dist.getNumericalMean(), 3.771428571428, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 14.816326530, tol);
    }
}

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