Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 1 | /* |
| 2 | * Licensed to the Apache Software Foundation (ASF) under one or more |
| 3 | * contributor license agreements. See the NOTICE file distributed with |
| 4 | * this work for additional information regarding copyright ownership. |
| 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 |
| 6 | * (the "License"); you may not use this file except in compliance with |
| 7 | * the License. You may obtain a copy of the License at |
| 8 | * |
| 9 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 10 | * |
| 11 | * Unless required by applicable law or agreed to in writing, software |
| 12 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 14 | * See the License for the specific language governing permissions and |
| 15 | * limitations under the License. |
| 16 | */ |
| 17 | |
| 18 | package org.apache.commons.math.distribution; |
| 19 | |
| 20 | import java.io.Serializable; |
| 21 | |
| 22 | import org.apache.commons.math.MathRuntimeException; |
| 23 | import org.apache.commons.math.exception.util.LocalizedFormats; |
| 24 | import org.apache.commons.math.util.MathUtils; |
| 25 | import org.apache.commons.math.util.FastMath; |
| 26 | |
| 27 | /** |
| 28 | * The default implementation of {@link HypergeometricDistribution}. |
| 29 | * |
| 30 | * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $ |
| 31 | */ |
| 32 | public class HypergeometricDistributionImpl extends AbstractIntegerDistribution |
| 33 | implements HypergeometricDistribution, Serializable { |
| 34 | |
| 35 | /** Serializable version identifier */ |
| 36 | private static final long serialVersionUID = -436928820673516179L; |
| 37 | |
| 38 | /** The number of successes in the population. */ |
| 39 | private int numberOfSuccesses; |
| 40 | |
| 41 | /** The population size. */ |
| 42 | private int populationSize; |
| 43 | |
| 44 | /** The sample size. */ |
| 45 | private int sampleSize; |
| 46 | |
| 47 | /** |
| 48 | * Construct a new hypergeometric distribution with the given the population |
| 49 | * size, the number of successes in the population, and the sample size. |
| 50 | * |
| 51 | * @param populationSize the population size. |
| 52 | * @param numberOfSuccesses number of successes in the population. |
| 53 | * @param sampleSize the sample size. |
| 54 | */ |
| 55 | public HypergeometricDistributionImpl(int populationSize, |
| 56 | int numberOfSuccesses, int sampleSize) { |
| 57 | super(); |
| 58 | if (numberOfSuccesses > populationSize) { |
| 59 | throw MathRuntimeException |
| 60 | .createIllegalArgumentException( |
| 61 | LocalizedFormats.NUMBER_OF_SUCCESS_LARGER_THAN_POPULATION_SIZE, |
| 62 | numberOfSuccesses, populationSize); |
| 63 | } |
| 64 | if (sampleSize > populationSize) { |
| 65 | throw MathRuntimeException |
| 66 | .createIllegalArgumentException( |
| 67 | LocalizedFormats.SAMPLE_SIZE_LARGER_THAN_POPULATION_SIZE, |
| 68 | sampleSize, populationSize); |
| 69 | } |
| 70 | |
| 71 | setPopulationSizeInternal(populationSize); |
| 72 | setSampleSizeInternal(sampleSize); |
| 73 | setNumberOfSuccessesInternal(numberOfSuccesses); |
| 74 | } |
| 75 | |
| 76 | /** |
| 77 | * For this distribution, X, this method returns P(X ≤ x). |
| 78 | * |
| 79 | * @param x the value at which the PDF is evaluated. |
| 80 | * @return PDF for this distribution. |
| 81 | */ |
| 82 | @Override |
| 83 | public double cumulativeProbability(int x) { |
| 84 | double ret; |
| 85 | |
| 86 | int[] domain = getDomain(populationSize, numberOfSuccesses, sampleSize); |
| 87 | if (x < domain[0]) { |
| 88 | ret = 0.0; |
| 89 | } else if (x >= domain[1]) { |
| 90 | ret = 1.0; |
| 91 | } else { |
| 92 | ret = innerCumulativeProbability(domain[0], x, 1, populationSize, |
| 93 | numberOfSuccesses, sampleSize); |
| 94 | } |
| 95 | |
| 96 | return ret; |
| 97 | } |
| 98 | |
| 99 | /** |
| 100 | * Return the domain for the given hypergeometric distribution parameters. |
| 101 | * |
| 102 | * @param n the population size. |
| 103 | * @param m number of successes in the population. |
| 104 | * @param k the sample size. |
| 105 | * @return a two element array containing the lower and upper bounds of the |
| 106 | * hypergeometric distribution. |
| 107 | */ |
| 108 | private int[] getDomain(int n, int m, int k) { |
| 109 | return new int[] { getLowerDomain(n, m, k), getUpperDomain(m, k) }; |
| 110 | } |
| 111 | |
| 112 | /** |
| 113 | * Access the domain value lower bound, based on <code>p</code>, used to |
| 114 | * bracket a PDF root. |
| 115 | * |
| 116 | * @param p the desired probability for the critical value |
| 117 | * @return domain value lower bound, i.e. P(X < <i>lower bound</i>) < |
| 118 | * <code>p</code> |
| 119 | */ |
| 120 | @Override |
| 121 | protected int getDomainLowerBound(double p) { |
| 122 | return getLowerDomain(populationSize, numberOfSuccesses, sampleSize); |
| 123 | } |
| 124 | |
| 125 | /** |
| 126 | * Access the domain value upper bound, based on <code>p</code>, used to |
| 127 | * bracket a PDF root. |
| 128 | * |
| 129 | * @param p the desired probability for the critical value |
| 130 | * @return domain value upper bound, i.e. P(X < <i>upper bound</i>) > |
| 131 | * <code>p</code> |
| 132 | */ |
| 133 | @Override |
| 134 | protected int getDomainUpperBound(double p) { |
| 135 | return getUpperDomain(sampleSize, numberOfSuccesses); |
| 136 | } |
| 137 | |
| 138 | /** |
| 139 | * Return the lowest domain value for the given hypergeometric distribution |
| 140 | * parameters. |
| 141 | * |
| 142 | * @param n the population size. |
| 143 | * @param m number of successes in the population. |
| 144 | * @param k the sample size. |
| 145 | * @return the lowest domain value of the hypergeometric distribution. |
| 146 | */ |
| 147 | private int getLowerDomain(int n, int m, int k) { |
| 148 | return FastMath.max(0, m - (n - k)); |
| 149 | } |
| 150 | |
| 151 | /** |
| 152 | * Access the number of successes. |
| 153 | * |
| 154 | * @return the number of successes. |
| 155 | */ |
| 156 | public int getNumberOfSuccesses() { |
| 157 | return numberOfSuccesses; |
| 158 | } |
| 159 | |
| 160 | /** |
| 161 | * Access the population size. |
| 162 | * |
| 163 | * @return the population size. |
| 164 | */ |
| 165 | public int getPopulationSize() { |
| 166 | return populationSize; |
| 167 | } |
| 168 | |
| 169 | /** |
| 170 | * Access the sample size. |
| 171 | * |
| 172 | * @return the sample size. |
| 173 | */ |
| 174 | public int getSampleSize() { |
| 175 | return sampleSize; |
| 176 | } |
| 177 | |
| 178 | /** |
| 179 | * Return the highest domain value for the given hypergeometric distribution |
| 180 | * parameters. |
| 181 | * |
| 182 | * @param m number of successes in the population. |
| 183 | * @param k the sample size. |
| 184 | * @return the highest domain value of the hypergeometric distribution. |
| 185 | */ |
| 186 | private int getUpperDomain(int m, int k) { |
| 187 | return FastMath.min(k, m); |
| 188 | } |
| 189 | |
| 190 | /** |
| 191 | * For this distribution, X, this method returns P(X = x). |
| 192 | * |
| 193 | * @param x the value at which the PMF is evaluated. |
| 194 | * @return PMF for this distribution. |
| 195 | */ |
| 196 | public double probability(int x) { |
| 197 | double ret; |
| 198 | |
| 199 | int[] domain = getDomain(populationSize, numberOfSuccesses, sampleSize); |
| 200 | if (x < domain[0] || x > domain[1]) { |
| 201 | ret = 0.0; |
| 202 | } else { |
| 203 | double p = (double) sampleSize / (double) populationSize; |
| 204 | double q = (double) (populationSize - sampleSize) / (double) populationSize; |
| 205 | double p1 = SaddlePointExpansion.logBinomialProbability(x, |
| 206 | numberOfSuccesses, p, q); |
| 207 | double p2 = |
| 208 | SaddlePointExpansion.logBinomialProbability(sampleSize - x, |
| 209 | populationSize - numberOfSuccesses, p, q); |
| 210 | double p3 = |
| 211 | SaddlePointExpansion.logBinomialProbability(sampleSize, populationSize, p, q); |
| 212 | ret = FastMath.exp(p1 + p2 - p3); |
| 213 | } |
| 214 | |
| 215 | return ret; |
| 216 | } |
| 217 | |
| 218 | /** |
| 219 | * For the distribution, X, defined by the given hypergeometric distribution |
| 220 | * parameters, this method returns P(X = x). |
| 221 | * |
| 222 | * @param n the population size. |
| 223 | * @param m number of successes in the population. |
| 224 | * @param k the sample size. |
| 225 | * @param x the value at which the PMF is evaluated. |
| 226 | * @return PMF for the distribution. |
| 227 | */ |
| 228 | private double probability(int n, int m, int k, int x) { |
| 229 | return FastMath.exp(MathUtils.binomialCoefficientLog(m, x) + |
| 230 | MathUtils.binomialCoefficientLog(n - m, k - x) - |
| 231 | MathUtils.binomialCoefficientLog(n, k)); |
| 232 | } |
| 233 | |
| 234 | /** |
| 235 | * Modify the number of successes. |
| 236 | * |
| 237 | * @param num the new number of successes. |
| 238 | * @throws IllegalArgumentException if <code>num</code> is negative. |
| 239 | * @deprecated as of 2.1 (class will become immutable in 3.0) |
| 240 | */ |
| 241 | @Deprecated |
| 242 | public void setNumberOfSuccesses(int num) { |
| 243 | setNumberOfSuccessesInternal(num); |
| 244 | } |
| 245 | |
| 246 | /** |
| 247 | * Modify the number of successes. |
| 248 | * |
| 249 | * @param num the new number of successes. |
| 250 | * @throws IllegalArgumentException if <code>num</code> is negative. |
| 251 | */ |
| 252 | private void setNumberOfSuccessesInternal(int num) { |
| 253 | if (num < 0) { |
| 254 | throw MathRuntimeException.createIllegalArgumentException( |
| 255 | LocalizedFormats.NEGATIVE_NUMBER_OF_SUCCESSES, num); |
| 256 | } |
| 257 | numberOfSuccesses = num; |
| 258 | } |
| 259 | |
| 260 | /** |
| 261 | * Modify the population size. |
| 262 | * |
| 263 | * @param size the new population size. |
| 264 | * @throws IllegalArgumentException if <code>size</code> is not positive. |
| 265 | * @deprecated as of 2.1 (class will become immutable in 3.0) |
| 266 | */ |
| 267 | @Deprecated |
| 268 | public void setPopulationSize(int size) { |
| 269 | setPopulationSizeInternal(size); |
| 270 | } |
| 271 | |
| 272 | /** |
| 273 | * Modify the population size. |
| 274 | * |
| 275 | * @param size the new population size. |
| 276 | * @throws IllegalArgumentException if <code>size</code> is not positive. |
| 277 | */ |
| 278 | private void setPopulationSizeInternal(int size) { |
| 279 | if (size <= 0) { |
| 280 | throw MathRuntimeException.createIllegalArgumentException( |
| 281 | LocalizedFormats.NOT_POSITIVE_POPULATION_SIZE, size); |
| 282 | } |
| 283 | populationSize = size; |
| 284 | } |
| 285 | |
| 286 | /** |
| 287 | * Modify the sample size. |
| 288 | * |
| 289 | * @param size the new sample size. |
| 290 | * @throws IllegalArgumentException if <code>size</code> is negative. |
| 291 | * @deprecated as of 2.1 (class will become immutable in 3.0) |
| 292 | */ |
| 293 | @Deprecated |
| 294 | public void setSampleSize(int size) { |
| 295 | setSampleSizeInternal(size); |
| 296 | } |
| 297 | /** |
| 298 | * Modify the sample size. |
| 299 | * |
| 300 | * @param size the new sample size. |
| 301 | * @throws IllegalArgumentException if <code>size</code> is negative. |
| 302 | */ |
| 303 | private void setSampleSizeInternal(int size) { |
| 304 | if (size < 0) { |
| 305 | throw MathRuntimeException.createIllegalArgumentException( |
| 306 | LocalizedFormats.NOT_POSITIVE_SAMPLE_SIZE, size); |
| 307 | } |
| 308 | sampleSize = size; |
| 309 | } |
| 310 | |
| 311 | /** |
| 312 | * For this distribution, X, this method returns P(X ≥ x). |
| 313 | * |
| 314 | * @param x the value at which the CDF is evaluated. |
| 315 | * @return upper tail CDF for this distribution. |
| 316 | * @since 1.1 |
| 317 | */ |
| 318 | public double upperCumulativeProbability(int x) { |
| 319 | double ret; |
| 320 | |
| 321 | final int[] domain = getDomain(populationSize, numberOfSuccesses, sampleSize); |
| 322 | if (x < domain[0]) { |
| 323 | ret = 1.0; |
| 324 | } else if (x > domain[1]) { |
| 325 | ret = 0.0; |
| 326 | } else { |
| 327 | ret = innerCumulativeProbability(domain[1], x, -1, populationSize, numberOfSuccesses, sampleSize); |
| 328 | } |
| 329 | |
| 330 | return ret; |
| 331 | } |
| 332 | |
| 333 | /** |
| 334 | * For this distribution, X, this method returns P(x0 ≤ X ≤ x1). This |
| 335 | * probability is computed by summing the point probabilities for the values |
| 336 | * x0, x0 + 1, x0 + 2, ..., x1, in the order directed by dx. |
| 337 | * |
| 338 | * @param x0 the inclusive, lower bound |
| 339 | * @param x1 the inclusive, upper bound |
| 340 | * @param dx the direction of summation. 1 indicates summing from x0 to x1. |
| 341 | * 0 indicates summing from x1 to x0. |
| 342 | * @param n the population size. |
| 343 | * @param m number of successes in the population. |
| 344 | * @param k the sample size. |
| 345 | * @return P(x0 ≤ X ≤ x1). |
| 346 | */ |
| 347 | private double innerCumulativeProbability(int x0, int x1, int dx, int n, |
| 348 | int m, int k) { |
| 349 | double ret = probability(n, m, k, x0); |
| 350 | while (x0 != x1) { |
| 351 | x0 += dx; |
| 352 | ret += probability(n, m, k, x0); |
| 353 | } |
| 354 | return ret; |
| 355 | } |
| 356 | |
| 357 | /** |
| 358 | * Returns the lower bound for the support for the distribution. |
| 359 | * |
| 360 | * For population size <code>N</code>, |
| 361 | * number of successes <code>m</code>, and |
| 362 | * sample size <code>n</code>, |
| 363 | * the lower bound of the support is |
| 364 | * <code>max(0, n + m - N)</code> |
| 365 | * |
| 366 | * @return lower bound of the support |
| 367 | * @since 2.2 |
| 368 | */ |
| 369 | public int getSupportLowerBound() { |
| 370 | return FastMath.max(0, |
| 371 | getSampleSize() + getNumberOfSuccesses() - getPopulationSize()); |
| 372 | } |
| 373 | |
| 374 | /** |
| 375 | * Returns the upper bound for the support of the distribution. |
| 376 | * |
| 377 | * For number of successes <code>m</code> and |
| 378 | * sample size <code>n</code>, |
| 379 | * the upper bound of the support is |
| 380 | * <code>min(m, n)</code> |
| 381 | * |
| 382 | * @return upper bound of the support |
| 383 | * @since 2.2 |
| 384 | */ |
| 385 | public int getSupportUpperBound() { |
| 386 | return FastMath.min(getNumberOfSuccesses(), getSampleSize()); |
| 387 | } |
| 388 | |
| 389 | /** |
| 390 | * Returns the mean. |
| 391 | * |
| 392 | * For population size <code>N</code>, |
| 393 | * number of successes <code>m</code>, and |
| 394 | * sample size <code>n</code>, the mean is |
| 395 | * <code>n * m / N</code> |
| 396 | * |
| 397 | * @return the mean |
| 398 | * @since 2.2 |
| 399 | */ |
| 400 | protected double getNumericalMean() { |
| 401 | return (double)(getSampleSize() * getNumberOfSuccesses()) / (double)getPopulationSize(); |
| 402 | } |
| 403 | |
| 404 | /** |
| 405 | * Returns the variance. |
| 406 | * |
| 407 | * For population size <code>N</code>, |
| 408 | * number of successes <code>m</code>, and |
| 409 | * sample size <code>n</code>, the variance is |
| 410 | * <code>[ n * m * (N - n) * (N - m) ] / [ N^2 * (N - 1) ]</code> |
| 411 | * |
| 412 | * @return the variance |
| 413 | * @since 2.2 |
| 414 | */ |
| 415 | public double getNumericalVariance() { |
| 416 | final double N = getPopulationSize(); |
| 417 | final double m = getNumberOfSuccesses(); |
| 418 | final double n = getSampleSize(); |
| 419 | return ( n * m * (N - n) * (N - m) ) / ( (N*N * (N - 1)) ); |
| 420 | } |
| 421 | } |