commons-statistics-distribution/src/test/java/org/apache/commons/statistics/distribution/WeibullDistributionTest.java

/*
 * 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.statistics.distribution;

import org.apache.commons.numbers.gamma.LogGamma;
import org.junit.jupiter.api.Assertions;
import org.junit.jupiter.api.BeforeEach;
import org.junit.jupiter.api.Test;

/**
 * Test cases for WeibullDistribution.
 * Extends ContinuousDistributionAbstractTest.  See class javadoc for
 * ContinuousDistributionAbstractTest for details.
 */
class WeibullDistributionTest extends ContinuousDistributionAbstractTest {

    @BeforeEach
    void customSetUp() {
        setTolerance(1e-10);
    }

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

    @Override
    public WeibullDistribution makeDistribution() {
        return new WeibullDistribution(1.2, 2.1);
    }

    @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};
    }

    @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};
    }

    @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};
    }

    @Override
    public double[] makeCumulativePrecisionTestPoints() {
        return new double[] {1e-14, 1e-15};
    }

    @Override
    public double[] makeCumulativePrecisionTestValues() {
        // These were created using WolframAlpha
        return new double[] {6.506341377907031e-18, 4.1052238780858223e-19};
    }

    @Override
    public double[] makeSurvivalPrecisionTestPoints() {
        return new double[] {45, 47.2};
    }

    @Override
    public double[] makeSurvivalPrecisionTestValues() {
        // These were created using WolframAlpha
        return new double[] {6.6352694710268576e-18, 6.444810903667567e-19};
    }

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

    @Test
    void testDensityAtSupportBounds() {
        final WeibullDistribution distribution = makeDistribution();
        Assertions.assertEquals(0.0, distribution.density(0));
        Assertions.assertEquals(0.0, distribution.density(Double.POSITIVE_INFINITY));
    }

    @Test
    void testInverseCumulativeProbabilitySmallPAccuracy() {
        final WeibullDistribution dist = new WeibullDistribution(2, 3);
        final 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:
        Assertions.assertEquals(9.48683298050514e-9, t, 1e-17);
    }

    @Test
    void testInverseCumulativeProbabilityExtremes() {
        setInverseCumulativeTestPoints(new double[] {0.0, 1.0});
        setInverseCumulativeTestValues(new double[] {0.0, Double.POSITIVE_INFINITY});
        verifyInverseCumulativeProbabilities();
    }

    @Test
    void testParameterAccessors() {
        final WeibullDistribution dist = new WeibullDistribution(1, 2);
        Assertions.assertEquals(1, dist.getShape());
        Assertions.assertEquals(2, dist.getScale());
    }

    @Test
    void testConstructorPrecondition1() {
        Assertions.assertThrows(DistributionException.class, () -> new WeibullDistribution(0, 2));
    }

    @Test
    void testConstructorPrecondition2() {
        Assertions.assertThrows(DistributionException.class, () -> new WeibullDistribution(1, 0));
    }

    @Test
    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 empirically: mean(rweibull(10000, 2.5, 3.5)))
        Assertions.assertEquals(3.5 * Math.exp(LogGamma.value(1 + (1 / 2.5))), dist.getMean(), tol);
        Assertions.assertEquals((3.5 * 3.5) *
                            Math.exp(LogGamma.value(1 + (2 / 2.5))) -
                            (dist.getMean() * dist.getMean()), dist.getVariance(), tol);

        dist = new WeibullDistribution(10.4, 2.222);
        Assertions.assertEquals(2.222 * Math.exp(LogGamma.value(1 + (1 / 10.4))), dist.getMean(), tol);
        Assertions.assertEquals((2.222 * 2.222) *
                            Math.exp(LogGamma.value(1 + (2 / 10.4))) -
                            (dist.getMean() * dist.getMean()), dist.getVariance(), tol);
    }
}