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.FastMath; |
| 26 | |
| 27 | /** |
| 28 | * The default implementation of {@link GammaDistribution}. |
| 29 | * |
| 30 | * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $ |
| 31 | */ |
| 32 | public class GammaDistributionImpl extends AbstractContinuousDistribution |
| 33 | implements GammaDistribution, Serializable { |
| 34 | |
| 35 | /** |
| 36 | * Default inverse cumulative probability accuracy |
| 37 | * @since 2.1 |
| 38 | */ |
| 39 | public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9; |
| 40 | |
| 41 | /** Serializable version identifier */ |
| 42 | private static final long serialVersionUID = -3239549463135430361L; |
| 43 | |
| 44 | /** The shape parameter. */ |
| 45 | private double alpha; |
| 46 | |
| 47 | /** The scale parameter. */ |
| 48 | private double beta; |
| 49 | |
| 50 | /** Inverse cumulative probability accuracy */ |
| 51 | private final double solverAbsoluteAccuracy; |
| 52 | |
| 53 | /** |
| 54 | * Create a new gamma distribution with the given alpha and beta values. |
| 55 | * @param alpha the shape parameter. |
| 56 | * @param beta the scale parameter. |
| 57 | */ |
| 58 | public GammaDistributionImpl(double alpha, double beta) { |
| 59 | this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY); |
| 60 | } |
| 61 | |
| 62 | /** |
| 63 | * Create a new gamma distribution with the given alpha and beta values. |
| 64 | * @param alpha the shape parameter. |
| 65 | * @param beta the scale parameter. |
| 66 | * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates |
| 67 | * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}) |
| 68 | * @since 2.1 |
| 69 | */ |
| 70 | public GammaDistributionImpl(double alpha, double beta, double inverseCumAccuracy) { |
| 71 | super(); |
| 72 | setAlphaInternal(alpha); |
| 73 | setBetaInternal(beta); |
| 74 | solverAbsoluteAccuracy = inverseCumAccuracy; |
| 75 | } |
| 76 | |
| 77 | /** |
| 78 | * For this distribution, X, this method returns P(X < x). |
| 79 | * |
| 80 | * The implementation of this method is based on: |
| 81 | * <ul> |
| 82 | * <li> |
| 83 | * <a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html"> |
| 84 | * Chi-Squared Distribution</a>, equation (9).</li> |
| 85 | * <li>Casella, G., & Berger, R. (1990). <i>Statistical Inference</i>. |
| 86 | * Belmont, CA: Duxbury Press.</li> |
| 87 | * </ul> |
| 88 | * |
| 89 | * @param x the value at which the CDF is evaluated. |
| 90 | * @return CDF for this distribution. |
| 91 | * @throws MathException if the cumulative probability can not be |
| 92 | * computed due to convergence or other numerical errors. |
| 93 | */ |
| 94 | public double cumulativeProbability(double x) throws MathException{ |
| 95 | double ret; |
| 96 | |
| 97 | if (x <= 0.0) { |
| 98 | ret = 0.0; |
| 99 | } else { |
| 100 | ret = Gamma.regularizedGammaP(alpha, x / beta); |
| 101 | } |
| 102 | |
| 103 | return ret; |
| 104 | } |
| 105 | |
| 106 | /** |
| 107 | * For this distribution, X, this method returns the critical point x, such |
| 108 | * that P(X < x) = <code>p</code>. |
| 109 | * <p> |
| 110 | * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p> |
| 111 | * |
| 112 | * @param p the desired probability |
| 113 | * @return x, such that P(X < x) = <code>p</code> |
| 114 | * @throws MathException if the inverse cumulative probability can not be |
| 115 | * computed due to convergence or other numerical errors. |
| 116 | * @throws IllegalArgumentException if <code>p</code> is not a valid |
| 117 | * probability. |
| 118 | */ |
| 119 | @Override |
| 120 | public double inverseCumulativeProbability(final double p) |
| 121 | throws MathException { |
| 122 | if (p == 0) { |
| 123 | return 0d; |
| 124 | } |
| 125 | if (p == 1) { |
| 126 | return Double.POSITIVE_INFINITY; |
| 127 | } |
| 128 | return super.inverseCumulativeProbability(p); |
| 129 | } |
| 130 | |
| 131 | /** |
| 132 | * Modify the shape parameter, alpha. |
| 133 | * @param alpha the new shape parameter. |
| 134 | * @throws IllegalArgumentException if <code>alpha</code> is not positive. |
| 135 | * @deprecated as of 2.1 (class will become immutable in 3.0) |
| 136 | */ |
| 137 | @Deprecated |
| 138 | public void setAlpha(double alpha) { |
| 139 | setAlphaInternal(alpha); |
| 140 | } |
| 141 | |
| 142 | /** |
| 143 | * Modify the shape parameter, alpha. |
| 144 | * @param newAlpha the new shape parameter. |
| 145 | * @throws IllegalArgumentException if <code>newAlpha</code> is not positive. |
| 146 | */ |
| 147 | private void setAlphaInternal(double newAlpha) { |
| 148 | if (newAlpha <= 0.0) { |
| 149 | throw MathRuntimeException.createIllegalArgumentException( |
| 150 | LocalizedFormats.NOT_POSITIVE_ALPHA, |
| 151 | newAlpha); |
| 152 | } |
| 153 | this.alpha = newAlpha; |
| 154 | } |
| 155 | |
| 156 | /** |
| 157 | * Access the shape parameter, alpha |
| 158 | * @return alpha. |
| 159 | */ |
| 160 | public double getAlpha() { |
| 161 | return alpha; |
| 162 | } |
| 163 | |
| 164 | /** |
| 165 | * Modify the scale parameter, beta. |
| 166 | * @param newBeta the new scale parameter. |
| 167 | * @throws IllegalArgumentException if <code>newBeta</code> is not positive. |
| 168 | * @deprecated as of 2.1 (class will become immutable in 3.0) |
| 169 | */ |
| 170 | @Deprecated |
| 171 | public void setBeta(double newBeta) { |
| 172 | setBetaInternal(newBeta); |
| 173 | } |
| 174 | |
| 175 | /** |
| 176 | * Modify the scale parameter, beta. |
| 177 | * @param newBeta the new scale parameter. |
| 178 | * @throws IllegalArgumentException if <code>newBeta</code> is not positive. |
| 179 | */ |
| 180 | private void setBetaInternal(double newBeta) { |
| 181 | if (newBeta <= 0.0) { |
| 182 | throw MathRuntimeException.createIllegalArgumentException( |
| 183 | LocalizedFormats.NOT_POSITIVE_BETA, |
| 184 | newBeta); |
| 185 | } |
| 186 | this.beta = newBeta; |
| 187 | } |
| 188 | |
| 189 | /** |
| 190 | * Access the scale parameter, beta |
| 191 | * @return beta. |
| 192 | */ |
| 193 | public double getBeta() { |
| 194 | return beta; |
| 195 | } |
| 196 | |
| 197 | /** |
| 198 | * Returns the probability density for a particular point. |
| 199 | * |
| 200 | * @param x The point at which the density should be computed. |
| 201 | * @return The pdf at point x. |
| 202 | */ |
| 203 | @Override |
| 204 | public double density(double x) { |
| 205 | if (x < 0) return 0; |
| 206 | return FastMath.pow(x / beta, alpha - 1) / beta * FastMath.exp(-x / beta) / FastMath.exp(Gamma.logGamma(alpha)); |
| 207 | } |
| 208 | |
| 209 | /** |
| 210 | * Return the probability density for a particular point. |
| 211 | * |
| 212 | * @param x The point at which the density should be computed. |
| 213 | * @return The pdf at point x. |
| 214 | * @deprecated |
| 215 | */ |
| 216 | @Deprecated |
| 217 | public double density(Double x) { |
| 218 | return density(x.doubleValue()); |
| 219 | } |
| 220 | |
| 221 | /** |
| 222 | * Access the domain value lower bound, based on <code>p</code>, used to |
| 223 | * bracket a CDF root. This method is used by |
| 224 | * {@link #inverseCumulativeProbability(double)} to find critical values. |
| 225 | * |
| 226 | * @param p the desired probability for the critical value |
| 227 | * @return domain value lower bound, i.e. |
| 228 | * P(X < <i>lower bound</i>) < <code>p</code> |
| 229 | */ |
| 230 | @Override |
| 231 | protected double getDomainLowerBound(double p) { |
| 232 | // TODO: try to improve on this estimate |
| 233 | return Double.MIN_VALUE; |
| 234 | } |
| 235 | |
| 236 | /** |
| 237 | * Access the domain value upper bound, based on <code>p</code>, used to |
| 238 | * bracket a CDF root. This method is used by |
| 239 | * {@link #inverseCumulativeProbability(double)} to find critical values. |
| 240 | * |
| 241 | * @param p the desired probability for the critical value |
| 242 | * @return domain value upper bound, i.e. |
| 243 | * P(X < <i>upper bound</i>) > <code>p</code> |
| 244 | */ |
| 245 | @Override |
| 246 | protected double getDomainUpperBound(double p) { |
| 247 | // TODO: try to improve on this estimate |
| 248 | // NOTE: gamma is skewed to the left |
| 249 | // NOTE: therefore, P(X < μ) > .5 |
| 250 | |
| 251 | double ret; |
| 252 | |
| 253 | if (p < .5) { |
| 254 | // use mean |
| 255 | ret = alpha * beta; |
| 256 | } else { |
| 257 | // use max value |
| 258 | ret = Double.MAX_VALUE; |
| 259 | } |
| 260 | |
| 261 | return ret; |
| 262 | } |
| 263 | |
| 264 | /** |
| 265 | * Access the initial domain value, 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 initial domain value |
| 271 | */ |
| 272 | @Override |
| 273 | protected double getInitialDomain(double p) { |
| 274 | // TODO: try to improve on this estimate |
| 275 | // Gamma is skewed to the left, therefore, P(X < μ) > .5 |
| 276 | |
| 277 | double ret; |
| 278 | |
| 279 | if (p < .5) { |
| 280 | // use 1/2 mean |
| 281 | ret = alpha * beta * .5; |
| 282 | } else { |
| 283 | // use mean |
| 284 | ret = alpha * beta; |
| 285 | } |
| 286 | |
| 287 | return ret; |
| 288 | } |
| 289 | |
| 290 | /** |
| 291 | * Return the absolute accuracy setting of the solver used to estimate |
| 292 | * inverse cumulative probabilities. |
| 293 | * |
| 294 | * @return the solver absolute accuracy |
| 295 | * @since 2.1 |
| 296 | */ |
| 297 | @Override |
| 298 | protected double getSolverAbsoluteAccuracy() { |
| 299 | return solverAbsoluteAccuracy; |
| 300 | } |
| 301 | |
| 302 | /** |
| 303 | * Returns the upper bound of the support for the distribution. |
| 304 | * |
| 305 | * The lower bound of the support is always 0, regardless of the parameters. |
| 306 | * |
| 307 | * @return lower bound of the support (always 0) |
| 308 | * @since 2.2 |
| 309 | */ |
| 310 | public double getSupportLowerBound() { |
| 311 | return 0; |
| 312 | } |
| 313 | |
| 314 | /** |
| 315 | * Returns the upper bound of the support for the distribution. |
| 316 | * |
| 317 | * The upper bound of the support is always positive infinity, |
| 318 | * regardless of the parameters. |
| 319 | * |
| 320 | * @return upper bound of the support (always Double.POSITIVE_INFINITY) |
| 321 | * @since 2.2 |
| 322 | */ |
| 323 | public double getSupportUpperBound() { |
| 324 | return Double.POSITIVE_INFINITY; |
| 325 | } |
| 326 | |
| 327 | /** |
| 328 | * Returns the mean. |
| 329 | * |
| 330 | * For shape parameter <code>alpha</code> and scale |
| 331 | * parameter <code>beta</code>, the mean is |
| 332 | * <code>alpha * beta</code> |
| 333 | * |
| 334 | * @return the mean |
| 335 | * @since 2.2 |
| 336 | */ |
| 337 | public double getNumericalMean() { |
| 338 | return getAlpha() * getBeta(); |
| 339 | } |
| 340 | |
| 341 | /** |
| 342 | * Returns the variance. |
| 343 | * |
| 344 | * For shape parameter <code>alpha</code> and scale |
| 345 | * parameter <code>beta</code>, the variance is |
| 346 | * <code>alpha * beta^2</code> |
| 347 | * |
| 348 | * @return the variance |
| 349 | * @since 2.2 |
| 350 | */ |
| 351 | public double getNumericalVariance() { |
| 352 | final double b = getBeta(); |
| 353 | return getAlpha() * b * b; |
| 354 | } |
| 355 | } |