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* 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.WeibullDistribution;
import org.apache.commons.math4.exception.NotStrictlyPositiveException;
import org.apache.commons.numbers.gamma.LogGamma;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
* Test cases for WeibullDistribution.
* Extends ContinuousDistributionAbstractTest. See class javadoc for
* ContinuousDistributionAbstractTest for details.
*
*/
public class WeibullDistributionTest extends RealDistributionAbstractTest {
//-------------- Implementations for abstract methods -----------------------
/** Creates the default continuous distribution instance to use in tests. */
@Override
public WeibullDistribution makeDistribution() {
return new WeibullDistribution(1.2, 2.1);
}
/** Creates the default cumulative probability distribution test input values */
@Override
public double[] makeCumulativeTestPoints() {
// quantiles computed using R version 2.9.2
return new double[] {0.00664355180993, 0.0454328283309, 0.0981162737374, 0.176713524579, 0.321946865392,
10.5115496887, 7.4976304671, 6.23205600701, 5.23968436955, 4.2079028257};
}
/** 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[] {0.180535929306, 0.262801138133, 0.301905425199, 0.330899152971,
0.353441418887, 0.000788590320203, 0.00737060094841, 0.0177576041516, 0.0343043442574, 0.065664589369};
}
//---------------------------- Additional test cases -------------------------
@Test
public void testInverseCumulativeProbabilitySmallPAccuracy() {
WeibullDistribution dist = new WeibullDistribution(2, 3);
double t = dist.inverseCumulativeProbability(1e-17);
// Analytically, answer is solution to 1e-17 = 1-exp(-(x/3)^2)
// x = sqrt(-9*log(1-1e-17))
// If we're not careful, answer will be 0. Answer below is computed with care in Octave:
Assert.assertEquals(9.48683298050514e-9, t, 1e-17);
}
@Test
public void testInverseCumulativeProbabilityExtremes() {
setInverseCumulativeTestPoints(new double[] {0.0, 1.0});
setInverseCumulativeTestValues(
new double[] {0.0, Double.POSITIVE_INFINITY});
verifyInverseCumulativeProbabilities();
}
@Test
public void testAlpha() {
WeibullDistribution dist = new WeibullDistribution(1, 2);
Assert.assertEquals(1, dist.getShape(), 0);
try {
new WeibullDistribution(0, 2);
Assert.fail("NotStrictlyPositiveException expected");
} catch (NotStrictlyPositiveException e) {
// Expected.
}
}
@Test
public void testBeta() {
WeibullDistribution dist = new WeibullDistribution(1, 2);
Assert.assertEquals(2, dist.getScale(), 0);
try {
new WeibullDistribution(1, 0);
Assert.fail("NotStrictlyPositiveException expected");
} catch (NotStrictlyPositiveException e) {
// Expected.
}
}
@Test
public void testMoments() {
final double tol = 1e-9;
WeibullDistribution dist;
dist = new WeibullDistribution(2.5, 3.5);
// In R: 3.5*gamma(1+(1/2.5)) (or emperically: mean(rweibull(10000, 2.5, 3.5)))
Assert.assertEquals(dist.getNumericalMean(), 3.5 * FastMath.exp(LogGamma.value(1 + (1 / 2.5))), tol);
Assert.assertEquals(dist.getNumericalVariance(), (3.5 * 3.5) *
FastMath.exp(LogGamma.value(1 + (2 / 2.5))) -
(dist.getNumericalMean() * dist.getNumericalMean()), tol);
dist = new WeibullDistribution(10.4, 2.222);
Assert.assertEquals(dist.getNumericalMean(), 2.222 * FastMath.exp(LogGamma.value(1 + (1 / 10.4))), tol);
Assert.assertEquals(dist.getNumericalVariance(), (2.222 * 2.222) *
FastMath.exp(LogGamma.value(1 + (2 / 10.4))) -
(dist.getNumericalMean() * dist.getNumericalMean()), tol);
}
}