/*
* 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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import org.apache.commons.math4.distribution.GammaDistribution;
import org.apache.commons.math4.exception.NotStrictlyPositiveException;
import org.apache.commons.numbers.gamma.LanczosApproximation;
import org.apache.commons.math4.stat.descriptive.SummaryStatistics;
import org.apache.commons.math4.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 -------------------------
@Test
public void testParameterAccessors() {
GammaDistribution distribution = (GammaDistribution) getDistribution();
Assert.assertEquals(4d, distribution.getShape(), 0);
Assert.assertEquals(2d, distribution.getScale(), 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 = LanczosApproximation.value(x);
double tmp = x + LanczosApproximation.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/math4/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");
}
}