| /* |
| * 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); |
| } |
| } |
