1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with this 4 * work for additional information regarding copyright ownership. The ASF 5 * licenses this file to You under the Apache License, Version 2.0 (the 6 * "License"); you may not use this file except in compliance with the License. 7 * You may obtain a copy of the License at 8 * http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law 9 * or agreed to in writing, software distributed under the License is 10 * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY 11 * KIND, either express or implied. See the License for the specific language 12 * governing permissions and limitations under the License. 13 */ 14 package org.apache.commons.math3.distribution; 15 16 import org.junit.Assert; 17 import org.junit.Test; 18 19 /** 20 * Test cases for BinomialDistribution. Extends IntegerDistributionAbstractTest. 21 * See class javadoc for IntegerDistributionAbstractTest for details. 22 * 23 */ 24 public class BinomialDistributionTest extends IntegerDistributionAbstractTest { 25 26 /** 27 * Constructor to override default tolerance. 28 */ BinomialDistributionTest()29 public BinomialDistributionTest() { 30 setTolerance(1e-12); 31 } 32 33 // -------------- Implementations for abstract methods 34 // ----------------------- 35 36 /** Creates the default discrete distribution instance to use in tests. */ 37 @Override makeDistribution()38 public IntegerDistribution makeDistribution() { 39 return new BinomialDistribution(10, 0.70); 40 } 41 42 /** Creates the default probability density test input values. */ 43 @Override makeDensityTestPoints()44 public int[] makeDensityTestPoints() { 45 return new int[] { -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 }; 46 } 47 48 /** 49 * Creates the default probability density test expected values. 50 * Reference values are from R, version 2.15.3. 51 */ 52 @Override makeDensityTestValues()53 public double[] makeDensityTestValues() { 54 return new double[] { 0d, 0.0000059049d, 0.000137781d, 0.0014467005, 55 0.009001692, 0.036756909, 0.1029193452, 0.200120949, 0.266827932, 56 0.2334744405, 0.121060821, 0.0282475249, 0d }; 57 } 58 59 /** Creates the default cumulative probability density test input values */ 60 @Override makeCumulativeTestPoints()61 public int[] makeCumulativeTestPoints() { 62 return makeDensityTestPoints(); 63 } 64 65 /** 66 * Creates the default cumulative probability density test expected values. 67 * Reference values are from R, version 2.15.3. 68 */ 69 @Override makeCumulativeTestValues()70 public double[] makeCumulativeTestValues() { 71 return new double[] { 0d, 5.9049e-06, 0.0001436859, 0.0015903864, 0.0105920784, 0.0473489874, 72 0.1502683326, 0.3503892816, 0.6172172136, 0.8506916541, 0.9717524751, 1d, 1d }; 73 } 74 75 /** Creates the default inverse cumulative probability test input values */ 76 @Override makeInverseCumulativeTestPoints()77 public double[] makeInverseCumulativeTestPoints() { 78 return new double[] { 0, 0.001d, 0.010d, 0.025d, 0.050d, 0.100d, 79 0.999d, 0.990d, 0.975d, 0.950d, 0.900d, 1 }; 80 } 81 82 /** 83 * Creates the default inverse cumulative probability density test expected 84 * values 85 */ 86 @Override makeInverseCumulativeTestValues()87 public int[] makeInverseCumulativeTestValues() { 88 return new int[] { 0, 2, 3, 4, 5, 5, 10, 10, 10, 9, 9, 10 }; 89 } 90 91 // ----------------- Additional test cases --------------------------------- 92 93 /** Test degenerate case p = 0 */ 94 @Test testDegenerate0()95 public void testDegenerate0() { 96 BinomialDistribution dist = new BinomialDistribution(5, 0.0d); 97 setDistribution(dist); 98 setCumulativeTestPoints(new int[] { -1, 0, 1, 5, 10 }); 99 setCumulativeTestValues(new double[] { 0d, 1d, 1d, 1d, 1d }); 100 setDensityTestPoints(new int[] { -1, 0, 1, 10, 11 }); 101 setDensityTestValues(new double[] { 0d, 1d, 0d, 0d, 0d }); 102 setInverseCumulativeTestPoints(new double[] { 0.1d, 0.5d }); 103 setInverseCumulativeTestValues(new int[] { 0, 0 }); 104 verifyDensities(); 105 verifyCumulativeProbabilities(); 106 verifyInverseCumulativeProbabilities(); 107 Assert.assertEquals(dist.getSupportLowerBound(), 0); 108 Assert.assertEquals(dist.getSupportUpperBound(), 0); 109 } 110 111 /** Test degenerate case p = 1 */ 112 @Test testDegenerate1()113 public void testDegenerate1() { 114 BinomialDistribution dist = new BinomialDistribution(5, 1.0d); 115 setDistribution(dist); 116 setCumulativeTestPoints(new int[] { -1, 0, 1, 2, 5, 10 }); 117 setCumulativeTestValues(new double[] { 0d, 0d, 0d, 0d, 1d, 1d }); 118 setDensityTestPoints(new int[] { -1, 0, 1, 2, 5, 10 }); 119 setDensityTestValues(new double[] { 0d, 0d, 0d, 0d, 1d, 0d }); 120 setInverseCumulativeTestPoints(new double[] { 0.1d, 0.5d }); 121 setInverseCumulativeTestValues(new int[] { 5, 5 }); 122 verifyDensities(); 123 verifyCumulativeProbabilities(); 124 verifyInverseCumulativeProbabilities(); 125 Assert.assertEquals(dist.getSupportLowerBound(), 5); 126 Assert.assertEquals(dist.getSupportUpperBound(), 5); 127 } 128 129 /** Test degenerate case n = 0 */ 130 @Test testDegenerate2()131 public void testDegenerate2() { 132 BinomialDistribution dist = new BinomialDistribution(0, 0.01d); 133 setDistribution(dist); 134 setCumulativeTestPoints(new int[] { -1, 0, 1, 2, 5, 10 }); 135 setCumulativeTestValues(new double[] { 0d, 1d, 1d, 1d, 1d, 1d }); 136 setDensityTestPoints(new int[] { -1, 0, 1, 2, 5, 10 }); 137 setDensityTestValues(new double[] { 0d, 1d, 0d, 0d, 0d, 0d }); 138 setInverseCumulativeTestPoints(new double[] { 0.1d, 0.5d }); 139 setInverseCumulativeTestValues(new int[] { 0, 0 }); 140 verifyDensities(); 141 verifyCumulativeProbabilities(); 142 verifyInverseCumulativeProbabilities(); 143 Assert.assertEquals(dist.getSupportLowerBound(), 0); 144 Assert.assertEquals(dist.getSupportUpperBound(), 0); 145 } 146 147 @Test testMoments()148 public void testMoments() { 149 final double tol = 1e-9; 150 BinomialDistribution dist; 151 152 dist = new BinomialDistribution(10, 0.5); 153 Assert.assertEquals(dist.getNumericalMean(), 10d * 0.5d, tol); 154 Assert.assertEquals(dist.getNumericalVariance(), 10d * 0.5d * 0.5d, tol); 155 156 dist = new BinomialDistribution(30, 0.3); 157 Assert.assertEquals(dist.getNumericalMean(), 30d * 0.3d, tol); 158 Assert.assertEquals(dist.getNumericalVariance(), 30d * 0.3d * (1d - 0.3d), tol); 159 } 160 161 @Test testMath718()162 public void testMath718() { 163 // for large trials the evaluation of ContinuedFraction was inaccurate 164 // do a sweep over several large trials to test if the current implementation is 165 // numerically stable. 166 167 for (int trials = 500000; trials < 20000000; trials += 100000) { 168 BinomialDistribution dist = new BinomialDistribution(trials, 0.5); 169 int p = dist.inverseCumulativeProbability(0.5); 170 Assert.assertEquals(trials / 2, p); 171 } 172 } 173 } 174