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22 package org.hipparchus.distribution.continuous;
23
24 import static org.junit.Assert.assertEquals;
25
26 import org.junit.Test;
27
28 public class BetaDistributionTest {
29
30 static final double[] alphaBetas = {0.1, 1, 10, 100, 1000};
31 static final double epsilon = 0.1;
32
33 @Test
34 public void testCumulative() {
35 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};
36
37 checkCumulative(0.1, 0.1,
38 x, new double[]{
39 0.0000000000, 0.0000000000, 0.4063850939, 0.4397091902, 0.4628041861,
40 0.4821200456, 0.5000000000, 0.5178799544, 0.5371958139, 0.5602908098,
41 0.5936149061, 1.0000000000, 1.0000000000});
42 checkCumulative(0.1, 0.5,
43 x, new double[]{
44 0.0000000000, 0.0000000000, 0.7048336221, 0.7593042194, 0.7951765304,
45 0.8234948385, 0.8480017124, 0.8706034370, 0.8926585878, 0.9156406404,
46 0.9423662883, 1.0000000000, 1.0000000000});
47 checkCumulative(0.1, 1.0,
48 x, new double[]{
49 0.0000000000, 0.0000000000, 0.7943282347, 0.8513399225, 0.8865681506,
50 0.9124435366, 0.9330329915, 0.9502002165, 0.9649610951, 0.9779327685,
51 0.9895192582, 1.0000000000, 1.0000000000});
52 checkCumulative(0.1, 2.0,
53 x, new double[]{
54 0.0000000000, 0.0000000000, 0.8658177758, 0.9194471163, 0.9486279211,
55 0.9671901487, 0.9796846411, 0.9882082252, 0.9939099280, 0.9974914239,
56 0.9994144508, 1.0000000000, 1.0000000000});
57 checkCumulative(0.1, 4.0,
58 x, new double[]{
59 0.0000000000, 0.0000000000, 0.9234991121, 0.9661958941, 0.9842285085,
60 0.9928444112, 0.9970040660, 0.9989112804, 0.9996895625, 0.9999440793,
61 0.9999967829, 1.0000000000, 1.0000000000});
62 checkCumulative(0.5, 0.1,
63 x, new double[]{
64 0.00000000000, 0.00000000000, 0.05763371168, 0.08435935962,
65 0.10734141216, 0.12939656302, 0.15199828760, 0.17650516146,
66 0.20482346963, 0.24069578055, 0.29516637795, 1.00000000000, 1.00000000000});
67
68 checkCumulative(0.5, 0.5,
69 x, new double[]{
70 0.0000000000, 0.0000000000, 0.2048327647, 0.2951672353, 0.3690101196,
71 0.4359057832, 0.5000000000, 0.5640942168, 0.6309898804, 0.7048327647,
72 0.7951672353, 1.0000000000, 1.0000000000});
73 checkCumulative(0.5, 1.0,
74 x, new double[]{
75 0.0000000000, 0.0000000000, 0.3162277660, 0.4472135955, 0.5477225575,
76 0.6324555320, 0.7071067812, 0.7745966692, 0.8366600265, 0.8944271910,
77 0.9486832981, 1.0000000000, 1.0000000000});
78 checkCumulative(0.5, 2.0,
79 x, new double[]{
80 0.0000000000, 0.0000000000, 0.4585302607, 0.6260990337, 0.7394254526,
81 0.8221921916, 0.8838834765, 0.9295160031, 0.9621590305, 0.9838699101,
82 0.9961174630, 1.0000000000, 1.0000000000});
83 checkCumulative(0.5, 4.0,
84 x, new double[]{
85 0.0000000000, 0.0000000000, 0.6266250826, 0.8049844719, 0.8987784842,
86 0.9502644369, 0.9777960959, 0.9914837366, 0.9974556254, 0.9995223859,
87 0.9999714889, 1.0000000000, 1.0000000000});
88 checkCumulative(1.0, 0.1,
89 x, new double[]{
90 0.00000000000, 0.00000000000, 0.01048074179, 0.02206723146,
91 0.03503890488, 0.04979978349, 0.06696700846, 0.08755646344,
92 0.11343184943, 0.14866007748, 0.20567176528, 1.00000000000, 1.00000000000});
93 checkCumulative(1.0, 0.5,
94 x, new double[]{
95 0.00000000000, 0.00000000000, 0.05131670195, 0.10557280900,
96 0.16333997347, 0.22540333076, 0.29289321881, 0.36754446797,
97 0.45227744249, 0.55278640450, 0.68377223398, 1.00000000000, 1.00000000000});
98 checkCumulative(1, 1,
99 x, new double[]{
100 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});
101 checkCumulative(1, 2,
102 x, new double[]{
103 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});
104 checkCumulative(1, 4,
105 x, new double[]{
106 0.0000, 0.0000, 0.3439, 0.5904, 0.7599, 0.8704, 0.9375, 0.9744, 0.9919,
107 0.9984, 0.9999, 1.0000, 1.0000});
108 checkCumulative(2.0, 0.1,
109 x, new double[]{
110 0.0000000000000, 0.0000000000000, 0.0005855492117, 0.0025085760862,
111 0.0060900720266, 0.0117917748341, 0.0203153588864, 0.0328098512512,
112 0.0513720788952, 0.0805528836776, 0.1341822241505, 1.0000000000000, 1.0000000000000});
113 checkCumulative(2, 1,
114 x, new double[]{
115 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});
116 checkCumulative(2.0, 0.5,
117 x, new double[]{
118 0.000000000000, 0.000000000000, 0.003882537047, 0.016130089900,
119 0.037840969486, 0.070483996910, 0.116116523517, 0.177807808356,
120 0.260574547368, 0.373900966300, 0.541469739276, 1.000000000000, 1.000000000000});
121 checkCumulative(2, 2,
122 x, new double[]{
123 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});
124 checkCumulative(2, 4,
125 x, new double[]{
126 0.00000, 0.00000, 0.08146, 0.26272, 0.47178, 0.66304, 0.81250, 0.91296,
127 0.96922, 0.99328, 0.99954, 1.00000, 1.00000});
128 checkCumulative(4.0, 0.1,
129 x, new double[]{
130 0.000000000e+00, 0.000000000e+00, 3.217128269e-06, 5.592070271e-05,
131 3.104375474e-04, 1.088719595e-03, 2.995933981e-03, 7.155588777e-03,
132 1.577149153e-02, 3.380410585e-02, 7.650088789e-02, 1.000000000e+00, 1.000000000e+00});
133 checkCumulative(4.0, 0.5,
134 x, new double[]{
135 0.000000000e+00, 0.000000000e+00, 2.851114863e-05, 4.776140576e-04,
136 2.544374616e-03, 8.516263371e-03, 2.220390414e-02, 4.973556312e-02,
137 1.012215158e-01, 1.950155281e-01, 3.733749174e-01, 1.000000000e+00, 1.000000000e+00});
138 checkCumulative(4, 1,
139 x, new double[]{
140 0.0000, 0.0000, 0.0001, 0.0016, 0.0081, 0.0256, 0.0625, 0.1296, 0.2401,
141 0.4096, 0.6561, 1.0000, 1.0000});
142 checkCumulative(4, 2,
143 x, new double[]{
144 0.00000, 0.00000, 0.00046, 0.00672, 0.03078, 0.08704, 0.18750, 0.33696,
145 0.52822, 0.73728, 0.91854, 1.00000, 1.00000});
146 checkCumulative(4, 4,
147 x, new double[]{
148 0.000000, 0.000000, 0.002728, 0.033344, 0.126036, 0.289792, 0.500000,
149 0.710208, 0.873964, 0.966656, 0.997272, 1.000000, 1.000000});
150
151 }
152
153 private void checkCumulative(double alpha, double beta, double[] x, double[] cumes) {
154 BetaDistribution d = new BetaDistribution(alpha, beta);
155 for (int i = 0; i < x.length; i++) {
156 assertEquals(cumes[i], d.cumulativeProbability(x[i]), 1e-8);
157 }
158
159 for (int i = 1; i < x.length - 1; i++) {
160 assertEquals(x[i], d.inverseCumulativeProbability(cumes[i]), 1e-5);
161 }
162 }
163
164 @Test
165 public void testDensity() {
166 double[] x = new double[]{1e-6, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9};
167 checkDensity(0.1, 0.1,
168 x, new double[]{
169 12741.2357380649, 0.4429889586665234, 2.639378715e-01, 2.066393611e-01,
170 1.832401831e-01, 1.766302780e-01, 1.832404579e-01, 2.066400696e-01,
171 2.639396531e-01, 4.429925026e-01});
172 checkDensity(0.1, 0.5,
173 x, new double[]{
174 2.218377102e+04, 7.394524202e-01, 4.203020268e-01, 3.119435533e-01,
175 2.600787829e-01, 2.330648626e-01, 2.211408259e-01, 2.222728708e-01,
176 2.414013907e-01, 3.070567405e-01});
177 checkDensity(0.1, 1.0,
178 x, new double[]{
179 2.511886432e+04, 7.943210858e-01, 4.256680458e-01, 2.955218303e-01,
180 2.281103709e-01, 1.866062624e-01, 1.583664652e-01, 1.378514078e-01,
181 1.222414585e-01, 1.099464743e-01});
182 checkDensity(0.1, 2.0,
183 x, new double[]{
184 2.763072312e+04, 7.863770012e-01, 3.745874120e-01, 2.275514842e-01,
185 1.505525939e-01, 1.026332391e-01, 6.968107049e-02, 4.549081293e-02,
186 2.689298641e-02, 1.209399123e-02});
187 checkDensity(0.1, 4.0,
188 x, new double[]{
189 2.997927462e+04, 6.911058917e-01, 2.601128486e-01, 1.209774010e-01,
190 5.880564714e-02, 2.783915474e-02, 1.209657335e-02, 4.442148268e-03,
191 1.167143939e-03, 1.312171805e-04});
192 checkDensity(0.5, 0.1,
193 x, new double[]{
194 88.3152184726, 0.3070542841, 0.2414007269, 0.2222727015,
195 0.2211409364, 0.2330652355, 0.2600795198, 0.3119449793,
196 0.4203052841, 0.7394649088});
197 checkDensity(0.5, 0.5,
198 x, new double[]{
199 318.3100453389, 1.0610282383, 0.7957732234, 0.6946084565,
200 0.6497470636, 0.6366197724, 0.6497476051, 0.6946097796,
201 0.7957762075, 1.0610376697});
202 checkDensity(0.5, 1.0,
203 x, new double[]{
204 500.0000000000, 1.5811309244, 1.1180311937, 0.9128694077,
205 0.7905684268, 0.7071060741, 0.6454966865, 0.5976138778,
206 0.5590166450, 0.5270459839});
207 checkDensity(0.5, 2.0,
208 x, new double[]{
209 749.99925000000, 2.134537420613655, 1.34163575536, 0.95851150881,
210 0.71151039830, 0.53032849490, 0.38729704363, 0.26892534859,
211 0.16770415497, 0.07905610701});
212 checkDensity(0.5, 4.0,
213 x, new double[]{
214 1.093746719e+03, 2.52142232809988, 1.252190241e+00, 6.849343920e-01,
215 3.735417140e-01, 1.933481570e-01, 9.036885833e-02, 3.529621669e-02,
216 9.782644546e-03, 1.152878503e-03});
217 checkDensity(1.0, 0.1,
218 x, new double[]{
219 0.1000000900, 0.1099466942, 0.1222417336, 0.1378517623, 0.1583669403,
220 0.1866069342, 0.2281113974, 0.2955236034, 0.4256718768,
221 0.7943353837});
222 checkDensity(1.0, 0.5,
223 x, new double[]{
224 0.5000002500, 0.5270465695, 0.5590173438, 0.5976147315, 0.6454977623,
225 0.7071074883, 0.7905704033, 0.9128724506,
226 1.1180367838, 1.5811467358});
227 checkDensity(1, 1,
228 x, new double[]{
229 1, 1, 1,
230 1, 1, 1, 1,
231 1, 1, 1});
232 checkDensity(1, 2,
233 x, new double[]{
234 1.999998, 1.799998, 1.599998, 1.399998, 1.199998, 0.999998, 0.799998,
235 0.599998, 0.399998,
236 0.199998});
237 checkDensity(1, 4,
238 x, new double[]{
239 3.999988000012, 2.915990280011, 2.047992320010, 1.371994120008,
240 0.863995680007, 0.499997000006, 0.255998080005, 0.107998920004,
241 0.031999520002, 0.003999880001});
242 checkDensity(2.0, 0.1,
243 x, new double[]{
244 1.100000990e-07, 1.209425730e-02, 2.689331586e-02, 4.549123318e-02,
245 6.968162794e-02, 1.026340191e-01, 1.505537732e-01, 2.275534997e-01,
246 3.745917198e-01, 7.863929037e-01});
247 checkDensity(2.0, 0.5,
248 x, new double[]{
249 7.500003750e-07, 7.905777599e-02, 1.677060417e-01, 2.689275256e-01,
250 3.872996256e-01, 5.303316769e-01, 7.115145488e-01, 9.585174425e-01,
251 1.341645818e+00, 2.134537420613655});
252 checkDensity(2, 1,
253 x, new double[]{
254 0.000002, 0.200002, 0.400002, 0.600002, 0.800002, 1.000002, 1.200002,
255 1.400002, 1.600002,
256 1.800002});
257 checkDensity(2, 2,
258 x, new double[]{
259 5.9999940e-06, 5.4000480e-01, 9.6000360e-01, 1.2600024e+00,
260 1.4400012e+00, 1.5000000e+00, 1.4399988e+00, 1.2599976e+00,
261 9.5999640e-01, 5.3999520e-01});
262 checkDensity(2, 4,
263 x, new double[]{
264 0.00001999994, 1.45800971996, 2.04800255997, 2.05799803998,
265 1.72799567999, 1.24999500000, 0.76799552000, 0.37799676001,
266 0.12799824001, 0.01799948000});
267 checkDensity(4.0, 0.1,
268 x, new double[]{
269 1.193501074e-19, 1.312253162e-04, 1.167181580e-03, 4.442248535e-03,
270 1.209679109e-02, 2.783958903e-02, 5.880649983e-02, 1.209791638e-01,
271 2.601171405e-01, 6.911229392e-01});
272 checkDensity(4.0, 0.5,
273 x, new double[]{
274 1.093750547e-18, 1.152948959e-03, 9.782950259e-03, 3.529697305e-02,
275 9.037036449e-02, 1.933508639e-01, 3.735463833e-01, 6.849425461e-01,
276 1.252205894e+00, 2.52142232809988});
277 checkDensity(4, 1,
278 x, new double[]{
279 4.000000000e-18, 4.000120001e-03, 3.200048000e-02, 1.080010800e-01,
280 2.560019200e-01, 5.000030000e-01, 8.640043200e-01, 1.372005880e+00,
281 2.048007680e+00, 2.916009720e+00});
282 checkDensity(4, 2,
283 x, new double[]{
284 1.999998000e-17, 1.800052000e-02, 1.280017600e-01, 3.780032400e-01,
285 7.680044800e-01, 1.250005000e+00, 1.728004320e+00, 2.058001960e+00,
286 2.047997440e+00, 1.457990280e+00});
287 checkDensity(4, 4,
288 x, new double[]{
289 1.399995800e-16, 1.020627216e-01, 5.734464512e-01, 1.296547409e+00,
290 1.935364838e+00, 2.187500000e+00, 1.935355162e+00, 1.296532591e+00,
291 5.734335488e-01, 1.020572784e-01});
292
293 }
294
295 private void checkDensity(double alpha, double beta, double[] x, double[] expected) {
296 BetaDistribution d = new BetaDistribution(alpha, beta);
297 for (int i = 0; i < x.length; i++) {
298 assertEquals(String.format("density at x=%.1f for alpha=%.1f, beta=%.1f", x[i], alpha, beta), expected[i], d.density(x[i]), 1e-5);
299 }
300 }
301
302 @Test
303 public void testMoments() {
304 final double tol = 1e-9;
305 BetaDistribution dist;
306
307 dist = new BetaDistribution(1, 1);
308 assertEquals(dist.getNumericalMean(), 0.5, tol);
309 assertEquals(dist.getNumericalVariance(), 1.0 / 12.0, tol);
310
311 dist = new BetaDistribution(2, 5);
312 assertEquals(dist.getNumericalMean(), 2.0 / 7.0, tol);
313 assertEquals(dist.getNumericalVariance(), 10.0 / (49.0 * 8.0), tol);
314 }
315
316 }