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.special.Gamma; 25 import org.apache.commons.math.util.FastMath; 26 27 /** 28 * Default implementation of 29 * {@link org.apache.commons.math.distribution.WeibullDistribution}. 30 * 31 * @since 1.1 32 * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $ 33 */ 34 public class WeibullDistributionImpl extends AbstractContinuousDistribution 35 implements WeibullDistribution, Serializable { 36 37 /** 38 * Default inverse cumulative probability accuracy 39 * @since 2.1 40 */ 41 public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9; 42 43 /** Serializable version identifier */ 44 private static final long serialVersionUID = 8589540077390120676L; 45 46 /** The shape parameter. */ 47 private double shape; 48 49 /** The scale parameter. */ 50 private double scale; 51 52 /** Inverse cumulative probability accuracy */ 53 private final double solverAbsoluteAccuracy; 54 55 /** Cached numerical mean */ 56 private double numericalMean = Double.NaN; 57 58 /** Whether or not the numerical mean has been calculated */ 59 private boolean numericalMeanIsCalculated = false; 60 61 /** Cached numerical variance */ 62 private double numericalVariance = Double.NaN; 63 64 /** Whether or not the numerical variance has been calculated */ 65 private boolean numericalVarianceIsCalculated = false; 66 67 /** 68 * Creates weibull distribution with the given shape and scale and a 69 * location equal to zero. 70 * @param alpha the shape parameter. 71 * @param beta the scale parameter. 72 */ 73 public WeibullDistributionImpl(double alpha, double beta){ 74 this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY); 75 } 76 77 /** 78 * Creates weibull distribution with the given shape, scale and inverse 79 * cumulative probability accuracy and a location equal to zero. 80 * @param alpha the shape parameter. 81 * @param beta the scale parameter. 82 * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates 83 * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}) 84 * @since 2.1 85 */ 86 public WeibullDistributionImpl(double alpha, double beta, double inverseCumAccuracy){ 87 super(); 88 setShapeInternal(alpha); 89 setScaleInternal(beta); 90 solverAbsoluteAccuracy = inverseCumAccuracy; 91 } 92 93 /** 94 * For this distribution, X, this method returns P(X < <code>x</code>). 95 * @param x the value at which the CDF is evaluated. 96 * @return CDF evaluated at <code>x</code>. 97 */ 98 public double cumulativeProbability(double x) { 99 double ret; 100 if (x <= 0.0) { 101 ret = 0.0; 102 } else { 103 ret = 1.0 - FastMath.exp(-FastMath.pow(x / scale, shape)); 104 } 105 return ret; 106 } 107 108 /** 109 * Access the shape parameter. 110 * @return the shape parameter. 111 */ 112 public double getShape() { 113 return shape; 114 } 115 116 /** 117 * Access the scale parameter. 118 * @return the scale parameter. 119 */ 120 public double getScale() { 121 return scale; 122 } 123 124 /** 125 * Returns the probability density for a particular point. 126 * 127 * @param x The point at which the density should be computed. 128 * @return The pdf at point x. 129 * @since 2.1 130 */ 131 @Override 132 public double density(double x) { 133 if (x < 0) { 134 return 0; 135 } 136 137 final double xscale = x / scale; 138 final double xscalepow = FastMath.pow(xscale, shape - 1); 139 140 /* 141 * FastMath.pow(x / scale, shape) = 142 * FastMath.pow(xscale, shape) = 143 * FastMath.pow(xscale, shape - 1) * xscale 144 */ 145 final double xscalepowshape = xscalepow * xscale; 146 147 return (shape / scale) * xscalepow * FastMath.exp(-xscalepowshape); 148 } 149 150 /** 151 * For this distribution, X, this method returns the critical point x, such 152 * that P(X < x) = <code>p</code>. 153 * <p> 154 * Returns <code>Double.NEGATIVE_INFINITY</code> for p=0 and 155 * <code>Double.POSITIVE_INFINITY</code> for p=1.</p> 156 * 157 * @param p the desired probability 158 * @return x, such that P(X < x) = <code>p</code> 159 * @throws IllegalArgumentException if <code>p</code> is not a valid 160 * probability. 161 */ 162 @Override 163 public double inverseCumulativeProbability(double p) { 164 double ret; 165 if (p < 0.0 || p > 1.0) { 166 throw MathRuntimeException.createIllegalArgumentException( 167 LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0); 168 } else if (p == 0) { 169 ret = 0.0; 170 } else if (p == 1) { 171 ret = Double.POSITIVE_INFINITY; 172 } else { 173 ret = scale * FastMath.pow(-FastMath.log(1.0 - p), 1.0 / shape); 174 } 175 return ret; 176 } 177 178 /** 179 * Modify the shape parameter. 180 * @param alpha the new shape parameter value. 181 * @deprecated as of 2.1 (class will become immutable in 3.0) 182 */ 183 @Deprecated 184 public void setShape(double alpha) { 185 setShapeInternal(alpha); 186 invalidateParameterDependentMoments(); 187 } 188 /** 189 * Modify the shape parameter. 190 * @param alpha the new shape parameter value. 191 */ 192 private void setShapeInternal(double alpha) { 193 if (alpha <= 0.0) { 194 throw MathRuntimeException.createIllegalArgumentException( 195 LocalizedFormats.NOT_POSITIVE_SHAPE, 196 alpha); 197 } 198 this.shape = alpha; 199 } 200 201 /** 202 * Modify the scale parameter. 203 * @param beta the new scale parameter value. 204 * @deprecated as of 2.1 (class will become immutable in 3.0) 205 */ 206 @Deprecated 207 public void setScale(double beta) { 208 setScaleInternal(beta); 209 invalidateParameterDependentMoments(); 210 } 211 /** 212 * Modify the scale parameter. 213 * @param beta the new scale parameter value. 214 */ 215 private void setScaleInternal(double beta) { 216 if (beta <= 0.0) { 217 throw MathRuntimeException.createIllegalArgumentException( 218 LocalizedFormats.NOT_POSITIVE_SCALE, 219 beta); 220 } 221 this.scale = beta; 222 } 223 224 /** 225 * Access the domain value lower bound, based on <code>p</code>, used to 226 * bracket a CDF root. This method is used by 227 * {@link #inverseCumulativeProbability(double)} to find critical values. 228 * 229 * @param p the desired probability for the critical value 230 * @return domain value lower bound, i.e. 231 * P(X < <i>lower bound</i>) < <code>p</code> 232 */ 233 @Override 234 protected double getDomainLowerBound(double p) { 235 return 0.0; 236 } 237 238 /** 239 * Access the domain value upper bound, based on <code>p</code>, used to 240 * bracket a CDF root. This method is used by 241 * {@link #inverseCumulativeProbability(double)} to find critical values. 242 * 243 * @param p the desired probability for the critical value 244 * @return domain value upper bound, i.e. 245 * P(X < <i>upper bound</i>) > <code>p</code> 246 */ 247 @Override 248 protected double getDomainUpperBound(double p) { 249 return Double.MAX_VALUE; 250 } 251 252 /** 253 * Access the initial domain value, based on <code>p</code>, used to 254 * bracket a CDF root. This method is used by 255 * {@link #inverseCumulativeProbability(double)} to find critical values. 256 * 257 * @param p the desired probability for the critical value 258 * @return initial domain value 259 */ 260 @Override 261 protected double getInitialDomain(double p) { 262 // use median 263 return FastMath.pow(scale * FastMath.log(2.0), 1.0 / shape); 264 } 265 266 /** 267 * Return the absolute accuracy setting of the solver used to estimate 268 * inverse cumulative probabilities. 269 * 270 * @return the solver absolute accuracy 271 * @since 2.1 272 */ 273 @Override 274 protected double getSolverAbsoluteAccuracy() { 275 return solverAbsoluteAccuracy; 276 } 277 278 /** 279 * Returns the lower bound of the support for the distribution. 280 * 281 * The lower bound of the support is always 0 no matter the parameters. 282 * 283 * @return lower bound of the support (always 0) 284 * @since 2.2 285 */ 286 public double getSupportLowerBound() { 287 return 0; 288 } 289 290 /** 291 * Returns the upper bound of the support for the distribution. 292 * 293 * The upper bound of the support is always positive infinity 294 * no matter the parameters. 295 * 296 * @return upper bound of the support (always Double.POSITIVE_INFINITY) 297 * @since 2.2 298 */ 299 public double getSupportUpperBound() { 300 return Double.POSITIVE_INFINITY; 301 } 302 303 /** 304 * Calculates the mean. 305 * 306 * The mean is <code>scale * Gamma(1 + (1 / shape))</code> 307 * where <code>Gamma(...)</code> is the Gamma-function 308 * 309 * @return the mean 310 * @since 2.2 311 */ 312 protected double calculateNumericalMean() { 313 final double sh = getShape(); 314 final double sc = getScale(); 315 316 return sc * FastMath.exp(Gamma.logGamma(1 + (1 / sh))); 317 } 318 319 /** 320 * Calculates the variance. 321 * 322 * The variance is 323 * <code>scale^2 * Gamma(1 + (2 / shape)) - mean^2</code> 324 * where <code>Gamma(...)</code> is the Gamma-function 325 * 326 * @return the variance 327 * @since 2.2 328 */ 329 private double calculateNumericalVariance() { 330 final double sh = getShape(); 331 final double sc = getScale(); 332 final double mn = getNumericalMean(); 333 334 return (sc * sc) * 335 FastMath.exp(Gamma.logGamma(1 + (2 / sh))) - 336 (mn * mn); 337 } 338 339 /** 340 * Returns the mean of the distribution. 341 * 342 * @return the mean or Double.NaN if it's not defined 343 * @since 2.2 344 */ 345 public double getNumericalMean() { 346 if (!numericalMeanIsCalculated) { 347 numericalMean = calculateNumericalMean(); 348 numericalMeanIsCalculated = true; 349 } 350 351 return numericalMean; 352 } 353 354 /** 355 * Returns the variance of the distribution. 356 * 357 * @return the variance (possibly Double.POSITIVE_INFINITY as 358 * for certain cases in {@link TDistributionImpl}) or 359 * Double.NaN if it's not defined 360 * @since 2.2 361 */ 362 public double getNumericalVariance() { 363 if (!numericalVarianceIsCalculated) { 364 numericalVariance = calculateNumericalVariance(); 365 numericalVarianceIsCalculated = true; 366 } 367 368 return numericalVariance; 369 } 370 371 /** 372 * Invalidates the cached mean and variance. 373 */ 374 private void invalidateParameterDependentMoments() { 375 numericalMeanIsCalculated = false; 376 numericalVarianceIsCalculated = false; 377 } 378 } 379
