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Java example source code file (BetaDistributionTest.java)

This example Java source code file (BetaDistributionTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

betadistribution, betadistributiontest, randomgenerator, realdistribution, string, suppresswarnings, test, util, var, well1024a, well19937a

The BetaDistributionTest.java Java example source code

/*
 * 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 java.util.Arrays;

import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well1024a;
import org.apache.commons.math3.random.Well19937a;
import org.apache.commons.math3.stat.StatUtils;
import org.apache.commons.math3.stat.inference.KolmogorovSmirnovTest;
import org.apache.commons.math3.stat.inference.TestUtils;
import org.junit.Assert;
import org.junit.Test;

public class BetaDistributionTest {

    static final double[] alphaBetas = {0.1, 1, 10, 100, 1000};
    static final double epsilon = StatUtils.min(alphaBetas);

    @Test
    public void testCumulative() {
        double[] x = new double[]{-0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1};
        // all test data computed using R 2.5
        checkCumulative(0.1, 0.1,
                x, new double[]{
                0.0000000000, 0.0000000000, 0.4063850939, 0.4397091902, 0.4628041861,
                0.4821200456, 0.5000000000, 0.5178799544, 0.5371958139, 0.5602908098,
                0.5936149061, 1.0000000000, 1.0000000000});
        checkCumulative(0.1, 0.5,
                x, new double[]{
                0.0000000000, 0.0000000000, 0.7048336221, 0.7593042194, 0.7951765304,
                0.8234948385, 0.8480017124, 0.8706034370, 0.8926585878, 0.9156406404,
                0.9423662883, 1.0000000000, 1.0000000000});
        checkCumulative(0.1, 1.0,
                x, new double[]{
                0.0000000000, 0.0000000000, 0.7943282347, 0.8513399225, 0.8865681506,
                0.9124435366, 0.9330329915, 0.9502002165, 0.9649610951, 0.9779327685,
                0.9895192582, 1.0000000000, 1.0000000000});
        checkCumulative(0.1, 2.0,
                x, new double[]{
                0.0000000000, 0.0000000000, 0.8658177758, 0.9194471163, 0.9486279211,
                0.9671901487, 0.9796846411, 0.9882082252, 0.9939099280, 0.9974914239,
                0.9994144508, 1.0000000000, 1.0000000000});
        checkCumulative(0.1, 4.0,
                x, new double[]{
                0.0000000000, 0.0000000000, 0.9234991121, 0.9661958941, 0.9842285085,
                0.9928444112, 0.9970040660, 0.9989112804, 0.9996895625, 0.9999440793,
                0.9999967829, 1.0000000000, 1.0000000000});
        checkCumulative(0.5, 0.1,
                x, new double[]{
                0.00000000000, 0.00000000000, 0.05763371168, 0.08435935962,
                0.10734141216, 0.12939656302, 0.15199828760, 0.17650516146,
                0.20482346963, 0.24069578055, 0.29516637795, 1.00000000000, 1.00000000000});

        checkCumulative(0.5, 0.5,
                x, new double[]{
                0.0000000000, 0.0000000000, 0.2048327647, 0.2951672353, 0.3690101196,
                0.4359057832, 0.5000000000, 0.5640942168, 0.6309898804, 0.7048327647,
                0.7951672353, 1.0000000000, 1.0000000000});
        checkCumulative(0.5, 1.0,
                x, new double[]{
                0.0000000000, 0.0000000000, 0.3162277660, 0.4472135955, 0.5477225575,
                0.6324555320, 0.7071067812, 0.7745966692, 0.8366600265, 0.8944271910,
                0.9486832981, 1.0000000000, 1.0000000000});
        checkCumulative(0.5, 2.0,
                x, new double[]{
                0.0000000000, 0.0000000000, 0.4585302607, 0.6260990337, 0.7394254526,
                0.8221921916, 0.8838834765, 0.9295160031, 0.9621590305, 0.9838699101,
                0.9961174630, 1.0000000000, 1.0000000000});
        checkCumulative(0.5, 4.0,
                x, new double[]{
                0.0000000000, 0.0000000000, 0.6266250826, 0.8049844719, 0.8987784842,
                0.9502644369, 0.9777960959, 0.9914837366, 0.9974556254, 0.9995223859,
                0.9999714889, 1.0000000000, 1.0000000000});
        checkCumulative(1.0, 0.1,
                x, new double[]{
                0.00000000000, 0.00000000000, 0.01048074179, 0.02206723146,
                0.03503890488, 0.04979978349, 0.06696700846, 0.08755646344,
                0.11343184943, 0.14866007748, 0.20567176528, 1.00000000000, 1.00000000000});
        checkCumulative(1.0, 0.5,
                x, new double[]{
                0.00000000000, 0.00000000000, 0.05131670195, 0.10557280900,
                0.16333997347, 0.22540333076, 0.29289321881, 0.36754446797,
                0.45227744249, 0.55278640450, 0.68377223398, 1.00000000000, 1.00000000000});
        checkCumulative(1, 1,
                x, new double[]{
                0.0, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.0});
        checkCumulative(1, 2,
                x, new double[]{
                0.00, 0.00, 0.19, 0.36, 0.51, 0.64, 0.75, 0.84, 0.91, 0.96, 0.99, 1.00, 1.00});
        checkCumulative(1, 4,
                x, new double[]{
                0.0000, 0.0000, 0.3439, 0.5904, 0.7599, 0.8704, 0.9375, 0.9744, 0.9919,
                0.9984, 0.9999, 1.0000, 1.0000});
        checkCumulative(2.0, 0.1,
                x, new double[]{
                0.0000000000000, 0.0000000000000, 0.0005855492117, 0.0025085760862,
                0.0060900720266, 0.0117917748341, 0.0203153588864, 0.0328098512512,
                0.0513720788952, 0.0805528836776, 0.1341822241505, 1.0000000000000, 1.0000000000000});
        checkCumulative(2, 1,
                x, new double[]{
                0.00, 0.00, 0.01, 0.04, 0.09, 0.16, 0.25, 0.36, 0.49, 0.64, 0.81, 1.00, 1.00});
        checkCumulative(2.0, 0.5,
                x, new double[]{
                0.000000000000, 0.000000000000, 0.003882537047, 0.016130089900,
                0.037840969486, 0.070483996910, 0.116116523517, 0.177807808356,
                0.260574547368, 0.373900966300, 0.541469739276, 1.000000000000, 1.000000000000});
        checkCumulative(2, 2,
                x, new double[]{
                0.000, 0.000, 0.028, 0.104, 0.216, 0.352, 0.500, 0.648, 0.784, 0.896, 0.972, 1.000, 1.000});
        checkCumulative(2, 4,
                x, new double[]{
                0.00000, 0.00000, 0.08146, 0.26272, 0.47178, 0.66304, 0.81250, 0.91296,
                0.96922, 0.99328, 0.99954, 1.00000, 1.00000});
        checkCumulative(4.0, 0.1,
                x, new double[]{
                0.000000000e+00, 0.000000000e+00, 3.217128269e-06, 5.592070271e-05,
                3.104375474e-04, 1.088719595e-03, 2.995933981e-03, 7.155588777e-03,
                1.577149153e-02, 3.380410585e-02, 7.650088789e-02, 1.000000000e+00, 1.000000000e+00});
        checkCumulative(4.0, 0.5,
                x, new double[]{
                0.000000000e+00, 0.000000000e+00, 2.851114863e-05, 4.776140576e-04,
                2.544374616e-03, 8.516263371e-03, 2.220390414e-02, 4.973556312e-02,
                1.012215158e-01, 1.950155281e-01, 3.733749174e-01, 1.000000000e+00, 1.000000000e+00});
        checkCumulative(4, 1,
                x, new double[]{
                0.0000, 0.0000, 0.0001, 0.0016, 0.0081, 0.0256, 0.0625, 0.1296, 0.2401,
                0.4096, 0.6561, 1.0000, 1.0000});
        checkCumulative(4, 2,
                x, new double[]{
                0.00000, 0.00000, 0.00046, 0.00672, 0.03078, 0.08704, 0.18750, 0.33696,
                0.52822, 0.73728, 0.91854, 1.00000, 1.00000});
        checkCumulative(4, 4,
                x, new double[]{
                0.000000, 0.000000, 0.002728, 0.033344, 0.126036, 0.289792, 0.500000,
                0.710208, 0.873964, 0.966656, 0.997272, 1.000000, 1.000000});

    }

    private void checkCumulative(double alpha, double beta, double[] x, double[] cumes) {
        BetaDistribution d = new BetaDistribution(alpha, beta);
        for (int i = 0; i < x.length; i++) {
            Assert.assertEquals(cumes[i], d.cumulativeProbability(x[i]), 1e-8);
        }

        for (int i = 1; i < x.length - 1; i++) {
            Assert.assertEquals(x[i], d.inverseCumulativeProbability(cumes[i]), 1e-5);
        }
    }

    @Test
    public void testDensity() {
        double[] x = new double[]{1e-6, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9};
        checkDensity(0.1, 0.1,
                x, new double[]{
                12741.2357380649, 0.4429889586665234, 2.639378715e-01, 2.066393611e-01,
                1.832401831e-01, 1.766302780e-01, 1.832404579e-01, 2.066400696e-01,
                2.639396531e-01, 4.429925026e-01});
        checkDensity(0.1, 0.5,
                x, new double[]{
                2.218377102e+04, 7.394524202e-01, 4.203020268e-01, 3.119435533e-01,
                2.600787829e-01, 2.330648626e-01, 2.211408259e-01, 2.222728708e-01,
                2.414013907e-01, 3.070567405e-01});
        checkDensity(0.1, 1.0,
                x, new double[]{
                2.511886432e+04, 7.943210858e-01, 4.256680458e-01, 2.955218303e-01,
                2.281103709e-01, 1.866062624e-01, 1.583664652e-01, 1.378514078e-01,
                1.222414585e-01, 1.099464743e-01});
        checkDensity(0.1, 2.0,
                x, new double[]{
                2.763072312e+04, 7.863770012e-01, 3.745874120e-01, 2.275514842e-01,
                1.505525939e-01, 1.026332391e-01, 6.968107049e-02, 4.549081293e-02,
                2.689298641e-02, 1.209399123e-02});
        checkDensity(0.1, 4.0,
                x, new double[]{
                2.997927462e+04, 6.911058917e-01, 2.601128486e-01, 1.209774010e-01,
                5.880564714e-02, 2.783915474e-02, 1.209657335e-02, 4.442148268e-03,
                1.167143939e-03, 1.312171805e-04});
        checkDensity(0.5, 0.1,
                x, new double[]{
                88.3152184726, 0.3070542841, 0.2414007269, 0.2222727015,
                0.2211409364, 0.2330652355, 0.2600795198, 0.3119449793,
                0.4203052841, 0.7394649088});
        checkDensity(0.5, 0.5,
                x, new double[]{
                318.3100453389, 1.0610282383, 0.7957732234, 0.6946084565,
                0.6497470636, 0.6366197724, 0.6497476051, 0.6946097796,
                0.7957762075, 1.0610376697});
        checkDensity(0.5, 1.0,
                x, new double[]{
                500.0000000000, 1.5811309244, 1.1180311937, 0.9128694077,
                0.7905684268, 0.7071060741, 0.6454966865, 0.5976138778,
                0.5590166450, 0.5270459839});
        checkDensity(0.5, 2.0,
                x, new double[]{
                749.99925000000, 2.134537420613655, 1.34163575536, 0.95851150881,
                0.71151039830, 0.53032849490, 0.38729704363, 0.26892534859,
                0.16770415497, 0.07905610701});
        checkDensity(0.5, 4.0,
                x, new double[]{
                1.093746719e+03, 2.52142232809988, 1.252190241e+00, 6.849343920e-01,
                3.735417140e-01, 1.933481570e-01, 9.036885833e-02, 3.529621669e-02,
                9.782644546e-03, 1.152878503e-03});
        checkDensity(1.0, 0.1,
                x, new double[]{
                0.1000000900, 0.1099466942, 0.1222417336, 0.1378517623, 0.1583669403,
                0.1866069342, 0.2281113974, 0.2955236034, 0.4256718768,
                0.7943353837});
        checkDensity(1.0, 0.5,
                x, new double[]{
                0.5000002500, 0.5270465695, 0.5590173438, 0.5976147315, 0.6454977623,
                0.7071074883, 0.7905704033, 0.9128724506,
                1.1180367838, 1.5811467358});
        checkDensity(1, 1,
                x, new double[]{
                1, 1, 1,
                1, 1, 1, 1,
                1, 1, 1});
        checkDensity(1, 2,
                x, new double[]{
                1.999998, 1.799998, 1.599998, 1.399998, 1.199998, 0.999998, 0.799998,
                0.599998, 0.399998,
                0.199998});
        checkDensity(1, 4,
                x, new double[]{
                3.999988000012, 2.915990280011, 2.047992320010, 1.371994120008,
                0.863995680007, 0.499997000006, 0.255998080005, 0.107998920004,
                0.031999520002, 0.003999880001});
        checkDensity(2.0, 0.1,
                x, new double[]{
                1.100000990e-07, 1.209425730e-02, 2.689331586e-02, 4.549123318e-02,
                6.968162794e-02, 1.026340191e-01, 1.505537732e-01, 2.275534997e-01,
                3.745917198e-01, 7.863929037e-01});
        checkDensity(2.0, 0.5,
                x, new double[]{
                7.500003750e-07, 7.905777599e-02, 1.677060417e-01, 2.689275256e-01,
                3.872996256e-01, 5.303316769e-01, 7.115145488e-01, 9.585174425e-01,
                1.341645818e+00, 2.134537420613655});
        checkDensity(2, 1,
                x, new double[]{
                0.000002, 0.200002, 0.400002, 0.600002, 0.800002, 1.000002, 1.200002,
                1.400002, 1.600002,
                1.800002});
        checkDensity(2, 2,
                x, new double[]{
                5.9999940e-06, 5.4000480e-01, 9.6000360e-01, 1.2600024e+00,
                1.4400012e+00, 1.5000000e+00, 1.4399988e+00, 1.2599976e+00,
                9.5999640e-01, 5.3999520e-01});
        checkDensity(2, 4,
                x, new double[]{
                0.00001999994, 1.45800971996, 2.04800255997, 2.05799803998,
                1.72799567999, 1.24999500000, 0.76799552000, 0.37799676001,
                0.12799824001, 0.01799948000});
        checkDensity(4.0, 0.1,
                x, new double[]{
                1.193501074e-19, 1.312253162e-04, 1.167181580e-03, 4.442248535e-03,
                1.209679109e-02, 2.783958903e-02, 5.880649983e-02, 1.209791638e-01,
                2.601171405e-01, 6.911229392e-01});
        checkDensity(4.0, 0.5,
                x, new double[]{
                1.093750547e-18, 1.152948959e-03, 9.782950259e-03, 3.529697305e-02,
                9.037036449e-02, 1.933508639e-01, 3.735463833e-01, 6.849425461e-01,
                1.252205894e+00, 2.52142232809988});
        checkDensity(4, 1,
                x, new double[]{
                4.000000000e-18, 4.000120001e-03, 3.200048000e-02, 1.080010800e-01,
                2.560019200e-01, 5.000030000e-01, 8.640043200e-01, 1.372005880e+00,
                2.048007680e+00, 2.916009720e+00});
        checkDensity(4, 2,
                x, new double[]{
                1.999998000e-17, 1.800052000e-02, 1.280017600e-01, 3.780032400e-01,
                7.680044800e-01, 1.250005000e+00, 1.728004320e+00, 2.058001960e+00,
                2.047997440e+00, 1.457990280e+00});
        checkDensity(4, 4,
                x, new double[]{
                1.399995800e-16, 1.020627216e-01, 5.734464512e-01, 1.296547409e+00,
                1.935364838e+00, 2.187500000e+00, 1.935355162e+00, 1.296532591e+00,
                5.734335488e-01, 1.020572784e-01});

    }

    @SuppressWarnings("boxing")
    private void checkDensity(double alpha, double beta, double[] x, double[] expected) {
        BetaDistribution d = new BetaDistribution(alpha, beta);
        for (int i = 0; i < x.length; i++) {
            Assert.assertEquals(String.format("density at x=%.1f for alpha=%.1f, beta=%.1f", x[i], alpha, beta), expected[i], d.density(x[i]), 1e-5);
        }
    }

    @Test
    public void testMoments() {
        final double tol = 1e-9;
        BetaDistribution dist;

        dist = new BetaDistribution(1, 1);
        Assert.assertEquals(dist.getNumericalMean(), 0.5, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 1.0 / 12.0, tol);

        dist = new BetaDistribution(2, 5);
        Assert.assertEquals(dist.getNumericalMean(), 2.0 / 7.0, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 10.0 / (49.0 * 8.0), tol);
    }

    @Test
    public void testMomentsSampling() {
        RandomGenerator random = new Well1024a(0x7829862c82fec2dal);
        final int numSamples = 1000;
        for (final double alpha : alphaBetas) {
            for (final double beta : alphaBetas) {
                final BetaDistribution betaDistribution = new BetaDistribution(random, alpha, beta);
                final double[] observed = new BetaDistribution(alpha, beta).sample(numSamples);
                Arrays.sort(observed);

                final String distribution = String.format("Beta(%.2f, %.2f)", alpha, beta);
                Assert.assertEquals(String.format("E[%s]", distribution),
                                    betaDistribution.getNumericalMean(),
                                    StatUtils.mean(observed), epsilon);
                Assert.assertEquals(String.format("Var[%s]", distribution),
                                    betaDistribution.getNumericalVariance(),
                                    StatUtils.variance(observed), epsilon);
            }
        }
    }

    @Test
    public void testGoodnessOfFit() {
        RandomGenerator random = new Well19937a(0x237db1db907b089fl);
        final int numSamples = 1000;
        final double level = 0.01;
        for (final double alpha : alphaBetas) {
            for (final double beta : alphaBetas) {
                final BetaDistribution betaDistribution = new BetaDistribution(random, alpha, beta);
                final double[] observed = betaDistribution.sample(numSamples);
                Assert.assertFalse("G goodness-of-fit test rejected null at alpha = " + level,
                                   gTest(betaDistribution, observed) < level);
                Assert.assertFalse("KS goodness-of-fit test rejected null at alpha = " + level,
                                   new KolmogorovSmirnovTest(random).kolmogorovSmirnovTest(betaDistribution, observed) < level);
            }
        }
    }

    private double gTest(final RealDistribution expectedDistribution, final double[] values) {
        final int numBins = values.length / 30;
        final double[] breaks = new double[numBins];
        for (int b = 0; b < breaks.length; b++) {
            breaks[b] = expectedDistribution.inverseCumulativeProbability((double) b / numBins);
        }

        final long[] observed = new long[numBins];
        for (final double value : values) {
            int b = 0;
            do {
                b++;
            } while (b < numBins && value >= breaks[b]);

            observed[b - 1]++;
        }

        final double[] expected = new double[numBins];
        Arrays.fill(expected, (double) values.length / numBins);

        return TestUtils.gTest(expected, observed);
    }
}

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