| /* |
| * 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); |
| } |
| } |