/*
* 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.math4.distribution;
import org.apache.commons.math4.distribution.ParetoDistribution;
import org.apache.commons.math4.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);
}
}