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18 package org.apache.commons.math.distribution;
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20 import org.apache.commons.math.MathException;
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29 public class NormalDistributionTest extends ContinuousDistributionAbstractTest {
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35 public NormalDistributionTest(String arg0) {
36 super(arg0);
37 }
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40
41
42 @Override
43 public ContinuousDistribution makeDistribution() {
44 return new NormalDistributionImpl(2.1, 1.4);
45 }
46
47
48 @Override
49 public double[] makeCumulativeTestPoints() {
50
51 return new double[] {-2.226325d, -1.156887d, -0.6439496d, -0.2027951d, 0.3058278d,
52 6.426325d, 5.356887d, 4.84395d, 4.402795d, 3.894172d};
53 }
54
55
56 @Override
57 public double[] makeCumulativeTestValues() {
58 return new double[] {0.001d, 0.01d, 0.025d, 0.05d, 0.1d, 0.999d,
59 0.990d, 0.975d, 0.950d, 0.900d};
60 }
61
62
63 @Override
64 protected void setUp() throws Exception {
65 super.setUp();
66 setTolerance(1E-6);
67 }
68
69
70
71 private void verifyQuantiles() throws Exception {
72 NormalDistribution distribution = (NormalDistribution) getDistribution();
73 double mu = distribution.getMean();
74 double sigma = distribution.getStandardDeviation();
75 setCumulativeTestPoints( new double[] {mu - 2 *sigma, mu - sigma,
76 mu, mu + sigma, mu +2 * sigma, mu +3 * sigma, mu + 4 * sigma,
77 mu + 5 * sigma});
78
79 setCumulativeTestValues(new double[] {0.02275013, 0.1586553, 0.5, 0.8413447,
80 0.9772499, 0.9986501, 0.9999683, 0.9999997});
81 verifyCumulativeProbabilities();
82 }
83
84 public void testQuantiles() throws Exception {
85 verifyQuantiles();
86 setDistribution(new NormalDistributionImpl(0, 1));
87 verifyQuantiles();
88 setDistribution(new NormalDistributionImpl(0, 0.1));
89 verifyQuantiles();
90 }
91
92 public void testInverseCumulativeProbabilityExtremes() throws Exception {
93 setInverseCumulativeTestPoints(new double[] {0, 1});
94 setInverseCumulativeTestValues(
95 new double[] {Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY});
96 verifyInverseCumulativeProbabilities();
97 }
98
99 public void testGetMean() {
100 NormalDistribution distribution = (NormalDistribution) getDistribution();
101 assertEquals(2.1, distribution.getMean(), 0);
102 }
103
104 public void testSetMean() throws Exception {
105 double mu = Math.random();
106 NormalDistribution distribution = (NormalDistribution) getDistribution();
107 distribution.setMean(mu);
108 verifyQuantiles();
109 }
110
111 public void testGetStandardDeviation() {
112 NormalDistribution distribution = (NormalDistribution) getDistribution();
113 assertEquals(1.4, distribution.getStandardDeviation(), 0);
114 }
115
116 public void testSetStandardDeviation() throws Exception {
117 double sigma = 0.1d + Math.random();
118 NormalDistribution distribution = (NormalDistribution) getDistribution();
119 distribution.setStandardDeviation(sigma);
120 assertEquals(sigma, distribution.getStandardDeviation(), 0);
121 verifyQuantiles();
122 try {
123 distribution.setStandardDeviation(0);
124 fail("Expecting IllegalArgumentException for sd = 0");
125 } catch (IllegalArgumentException ex) {
126
127 }
128 }
129
130 public void testDensity() {
131 double [] x = new double[]{-2, -1, 0, 1, 2};
132
133 checkDensity(0, 1, x, new double[]{0.05399096651, 0.24197072452, 0.39894228040, 0.24197072452, 0.05399096651});
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135 checkDensity(1.1, 1, x, new double[]{0.003266819056,0.043983595980,0.217852177033,0.396952547477,0.266085249899});
136 }
137
138 private void checkDensity(double mean, double sd, double[] x, double[] expected) {
139 NormalDistribution d = new NormalDistributionImpl(mean, sd);
140 for (int i = 0; i < x.length; i++) {
141 assertEquals(expected[i], d.density(x[i]), 1e-9);
142 }
143 }
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149 public void testExtremeValues() throws Exception {
150 NormalDistribution distribution = (NormalDistribution) getDistribution();
151 distribution.setMean(0);
152 distribution.setStandardDeviation(1);
153 for (int i = 0; i < 100; i+=5) {
154 double lowerTail = distribution.cumulativeProbability(-i);
155 double upperTail = distribution.cumulativeProbability(i);
156 if (i < 10) {
157 assertTrue(lowerTail > 0.0d);
158 assertTrue(upperTail < 1.0d);
159 }
160 else {
161 assertTrue(lowerTail < 0.00001);
162 assertTrue(upperTail > 0.99999);
163 }
164 }
165 }
166
167 public void testMath280() throws MathException {
168 NormalDistribution normal = new NormalDistributionImpl(0,1);
169 double result = normal.inverseCumulativeProbability(0.9772498680518209);
170 assertEquals(2.0, result, 1.0e-12);
171 }
172
173 }