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 | package org.apache.commons.math.distribution; |
| 18 | |
| 19 | import java.io.Serializable; |
| 20 | |
| 21 | import org.apache.commons.math.MathException; |
| 22 | import org.apache.commons.math.MathRuntimeException; |
| 23 | import org.apache.commons.math.exception.util.LocalizedFormats; |
| 24 | import org.apache.commons.math.special.Gamma; |
| 25 | import org.apache.commons.math.util.MathUtils; |
| 26 | import org.apache.commons.math.util.FastMath; |
| 27 | |
| 28 | /** |
| 29 | * Implementation for the {@link PoissonDistribution}. |
| 30 | * |
| 31 | * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $ |
| 32 | */ |
| 33 | public class PoissonDistributionImpl extends AbstractIntegerDistribution |
| 34 | implements PoissonDistribution, Serializable { |
| 35 | |
| 36 | /** |
| 37 | * Default maximum number of iterations for cumulative probability calculations. |
| 38 | * @since 2.1 |
| 39 | */ |
| 40 | public static final int DEFAULT_MAX_ITERATIONS = 10000000; |
| 41 | |
| 42 | /** |
| 43 | * Default convergence criterion. |
| 44 | * @since 2.1 |
| 45 | */ |
| 46 | public static final double DEFAULT_EPSILON = 1E-12; |
| 47 | |
| 48 | /** Serializable version identifier */ |
| 49 | private static final long serialVersionUID = -3349935121172596109L; |
| 50 | |
| 51 | /** Distribution used to compute normal approximation. */ |
| 52 | private NormalDistribution normal; |
| 53 | |
| 54 | /** |
| 55 | * Holds the Poisson mean for the distribution. |
| 56 | */ |
| 57 | private double mean; |
| 58 | |
| 59 | /** |
| 60 | * Maximum number of iterations for cumulative probability. |
| 61 | * |
| 62 | * Cumulative probabilities are estimated using either Lanczos series approximation of |
| 63 | * Gamma#regularizedGammaP or continued fraction approximation of Gamma#regularizedGammaQ. |
| 64 | */ |
| 65 | private int maxIterations = DEFAULT_MAX_ITERATIONS; |
| 66 | |
| 67 | /** |
| 68 | * Convergence criterion for cumulative probability. |
| 69 | */ |
| 70 | private double epsilon = DEFAULT_EPSILON; |
| 71 | |
| 72 | /** |
| 73 | * Create a new Poisson distribution with the given the mean. The mean value |
| 74 | * must be positive; otherwise an <code>IllegalArgument</code> is thrown. |
| 75 | * |
| 76 | * @param p the Poisson mean |
| 77 | * @throws IllegalArgumentException if p ≤ 0 |
| 78 | */ |
| 79 | public PoissonDistributionImpl(double p) { |
| 80 | this(p, new NormalDistributionImpl()); |
| 81 | } |
| 82 | |
| 83 | /** |
| 84 | * Create a new Poisson distribution with the given mean, convergence criterion |
| 85 | * and maximum number of iterations. |
| 86 | * |
| 87 | * @param p the Poisson mean |
| 88 | * @param epsilon the convergence criteria for cumulative probabilites |
| 89 | * @param maxIterations the maximum number of iterations for cumulative probabilites |
| 90 | * @since 2.1 |
| 91 | */ |
| 92 | public PoissonDistributionImpl(double p, double epsilon, int maxIterations) { |
| 93 | setMean(p); |
| 94 | this.epsilon = epsilon; |
| 95 | this.maxIterations = maxIterations; |
| 96 | } |
| 97 | |
| 98 | /** |
| 99 | * Create a new Poisson distribution with the given mean and convergence criterion. |
| 100 | * |
| 101 | * @param p the Poisson mean |
| 102 | * @param epsilon the convergence criteria for cumulative probabilites |
| 103 | * @since 2.1 |
| 104 | */ |
| 105 | public PoissonDistributionImpl(double p, double epsilon) { |
| 106 | setMean(p); |
| 107 | this.epsilon = epsilon; |
| 108 | } |
| 109 | |
| 110 | /** |
| 111 | * Create a new Poisson distribution with the given mean and maximum number of iterations. |
| 112 | * |
| 113 | * @param p the Poisson mean |
| 114 | * @param maxIterations the maximum number of iterations for cumulative probabilites |
| 115 | * @since 2.1 |
| 116 | */ |
| 117 | public PoissonDistributionImpl(double p, int maxIterations) { |
| 118 | setMean(p); |
| 119 | this.maxIterations = maxIterations; |
| 120 | } |
| 121 | |
| 122 | |
| 123 | /** |
| 124 | * Create a new Poisson distribution with the given the mean. The mean value |
| 125 | * must be positive; otherwise an <code>IllegalArgument</code> is thrown. |
| 126 | * |
| 127 | * @param p the Poisson mean |
| 128 | * @param z a normal distribution used to compute normal approximations. |
| 129 | * @throws IllegalArgumentException if p ≤ 0 |
| 130 | * @since 1.2 |
| 131 | * @deprecated as of 2.1 (to avoid possibly inconsistent state, the |
| 132 | * "NormalDistribution" will be instantiated internally) |
| 133 | */ |
| 134 | @Deprecated |
| 135 | public PoissonDistributionImpl(double p, NormalDistribution z) { |
| 136 | super(); |
| 137 | setNormalAndMeanInternal(z, p); |
| 138 | } |
| 139 | |
| 140 | /** |
| 141 | * Get the Poisson mean for the distribution. |
| 142 | * |
| 143 | * @return the Poisson mean for the distribution. |
| 144 | */ |
| 145 | public double getMean() { |
| 146 | return mean; |
| 147 | } |
| 148 | |
| 149 | /** |
| 150 | * Set the Poisson mean for the distribution. The mean value must be |
| 151 | * positive; otherwise an <code>IllegalArgument</code> is thrown. |
| 152 | * |
| 153 | * @param p the Poisson mean value |
| 154 | * @throws IllegalArgumentException if p ≤ 0 |
| 155 | * @deprecated as of 2.1 (class will become immutable in 3.0) |
| 156 | */ |
| 157 | @Deprecated |
| 158 | public void setMean(double p) { |
| 159 | setNormalAndMeanInternal(normal, p); |
| 160 | } |
| 161 | /** |
| 162 | * Set the Poisson mean for the distribution. The mean value must be |
| 163 | * positive; otherwise an <code>IllegalArgument</code> is thrown. |
| 164 | * |
| 165 | * @param z the new distribution |
| 166 | * @param p the Poisson mean value |
| 167 | * @throws IllegalArgumentException if p ≤ 0 |
| 168 | */ |
| 169 | private void setNormalAndMeanInternal(NormalDistribution z, |
| 170 | double p) { |
| 171 | if (p <= 0) { |
| 172 | throw MathRuntimeException.createIllegalArgumentException( |
| 173 | LocalizedFormats.NOT_POSITIVE_POISSON_MEAN, p); |
| 174 | } |
| 175 | mean = p; |
| 176 | normal = z; |
| 177 | normal.setMean(p); |
| 178 | normal.setStandardDeviation(FastMath.sqrt(p)); |
| 179 | } |
| 180 | |
| 181 | /** |
| 182 | * The probability mass function P(X = x) for a Poisson distribution. |
| 183 | * |
| 184 | * @param x the value at which the probability density function is |
| 185 | * evaluated. |
| 186 | * @return the value of the probability mass function at x |
| 187 | */ |
| 188 | public double probability(int x) { |
| 189 | double ret; |
| 190 | if (x < 0 || x == Integer.MAX_VALUE) { |
| 191 | ret = 0.0; |
| 192 | } else if (x == 0) { |
| 193 | ret = FastMath.exp(-mean); |
| 194 | } else { |
| 195 | ret = FastMath.exp(-SaddlePointExpansion.getStirlingError(x) - |
| 196 | SaddlePointExpansion.getDeviancePart(x, mean)) / |
| 197 | FastMath.sqrt(MathUtils.TWO_PI * x); |
| 198 | } |
| 199 | return ret; |
| 200 | } |
| 201 | |
| 202 | /** |
| 203 | * The probability distribution function P(X <= x) for a Poisson |
| 204 | * distribution. |
| 205 | * |
| 206 | * @param x the value at which the PDF is evaluated. |
| 207 | * @return Poisson distribution function evaluated at x |
| 208 | * @throws MathException if the cumulative probability can not be computed |
| 209 | * due to convergence or other numerical errors. |
| 210 | */ |
| 211 | @Override |
| 212 | public double cumulativeProbability(int x) throws MathException { |
| 213 | if (x < 0) { |
| 214 | return 0; |
| 215 | } |
| 216 | if (x == Integer.MAX_VALUE) { |
| 217 | return 1; |
| 218 | } |
| 219 | return Gamma.regularizedGammaQ((double) x + 1, mean, epsilon, maxIterations); |
| 220 | } |
| 221 | |
| 222 | /** |
| 223 | * Calculates the Poisson distribution function using a normal |
| 224 | * approximation. The <code>N(mean, sqrt(mean))</code> distribution is used |
| 225 | * to approximate the Poisson distribution. |
| 226 | * <p> |
| 227 | * The computation uses "half-correction" -- evaluating the normal |
| 228 | * distribution function at <code>x + 0.5</code> |
| 229 | * </p> |
| 230 | * |
| 231 | * @param x the upper bound, inclusive |
| 232 | * @return the distribution function value calculated using a normal |
| 233 | * approximation |
| 234 | * @throws MathException if an error occurs computing the normal |
| 235 | * approximation |
| 236 | */ |
| 237 | public double normalApproximateProbability(int x) throws MathException { |
| 238 | // calculate the probability using half-correction |
| 239 | return normal.cumulativeProbability(x + 0.5); |
| 240 | } |
| 241 | |
| 242 | /** |
| 243 | * Generates a random value sampled from this distribution. |
| 244 | * |
| 245 | * <p><strong>Algorithm Description</strong>: |
| 246 | * <ul><li> For small means, uses simulation of a Poisson process |
| 247 | * using Uniform deviates, as described |
| 248 | * <a href="http://irmi.epfl.ch/cmos/Pmmi/interactive/rng7.htm"> here.</a> |
| 249 | * The Poisson process (and hence value returned) is bounded by 1000 * mean.</li>< |
| 250 | * |
| 251 | * <li> For large means, uses the rejection algorithm described in <br/> |
| 252 | * Devroye, Luc. (1981).<i>The Computer Generation of Poisson Random Variables</i> |
| 253 | * <strong>Computing</strong> vol. 26 pp. 197-207.</li></ul></p> |
| 254 | * |
| 255 | * @return random value |
| 256 | * @since 2.2 |
| 257 | * @throws MathException if an error occurs generating the random value |
| 258 | */ |
| 259 | @Override |
| 260 | public int sample() throws MathException { |
| 261 | return (int) FastMath.min(randomData.nextPoisson(mean), Integer.MAX_VALUE); |
| 262 | } |
| 263 | |
| 264 | /** |
| 265 | * Access the domain value lower bound, based on <code>p</code>, used to |
| 266 | * bracket a CDF root. This method is used by |
| 267 | * {@link #inverseCumulativeProbability(double)} to find critical values. |
| 268 | * |
| 269 | * @param p the desired probability for the critical value |
| 270 | * @return domain lower bound |
| 271 | */ |
| 272 | @Override |
| 273 | protected int getDomainLowerBound(double p) { |
| 274 | return 0; |
| 275 | } |
| 276 | |
| 277 | /** |
| 278 | * Access the domain value upper bound, based on <code>p</code>, used to |
| 279 | * bracket a CDF root. This method is used by |
| 280 | * {@link #inverseCumulativeProbability(double)} to find critical values. |
| 281 | * |
| 282 | * @param p the desired probability for the critical value |
| 283 | * @return domain upper bound |
| 284 | */ |
| 285 | @Override |
| 286 | protected int getDomainUpperBound(double p) { |
| 287 | return Integer.MAX_VALUE; |
| 288 | } |
| 289 | |
| 290 | /** |
| 291 | * Modify the normal distribution used to compute normal approximations. The |
| 292 | * caller is responsible for insuring the normal distribution has the proper |
| 293 | * parameter settings. |
| 294 | * |
| 295 | * @param value the new distribution |
| 296 | * @since 1.2 |
| 297 | * @deprecated as of 2.1 (class will become immutable in 3.0) |
| 298 | */ |
| 299 | @Deprecated |
| 300 | public void setNormal(NormalDistribution value) { |
| 301 | setNormalAndMeanInternal(value, mean); |
| 302 | } |
| 303 | |
| 304 | /** |
| 305 | * Returns the lower bound of the support for the distribution. |
| 306 | * |
| 307 | * The lower bound of the support is always 0 no matter the mean parameter. |
| 308 | * |
| 309 | * @return lower bound of the support (always 0) |
| 310 | * @since 2.2 |
| 311 | */ |
| 312 | public int getSupportLowerBound() { |
| 313 | return 0; |
| 314 | } |
| 315 | |
| 316 | /** |
| 317 | * Returns the upper bound of the support for the distribution. |
| 318 | * |
| 319 | * The upper bound of the support is positive infinity, |
| 320 | * regardless of the parameter values. There is no integer infinity, |
| 321 | * so this method returns <code>Integer.MAX_VALUE</code> and |
| 322 | * {@link #isSupportUpperBoundInclusive()} returns <code>true</code>. |
| 323 | * |
| 324 | * @return upper bound of the support (always <code>Integer.MAX_VALUE</code> for positive infinity) |
| 325 | * @since 2.2 |
| 326 | */ |
| 327 | public int getSupportUpperBound() { |
| 328 | return Integer.MAX_VALUE; |
| 329 | } |
| 330 | |
| 331 | /** |
| 332 | * Returns the variance of the distribution. |
| 333 | * |
| 334 | * For mean parameter <code>p</code>, the variance is <code>p</code> |
| 335 | * |
| 336 | * @return the variance |
| 337 | * @since 2.2 |
| 338 | */ |
| 339 | public double getNumericalVariance() { |
| 340 | return getMean(); |
| 341 | } |
| 342 | |
| 343 | } |