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.Beta; 25 import org.apache.commons.math.util.FastMath; 26 27 /** 28 * Default implementation of 29 * {@link org.apache.commons.math.distribution.FDistribution}. 30 * 31 * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $ 32 */ 33 public class FDistributionImpl 34 extends AbstractContinuousDistribution 35 implements FDistribution, 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 = -8516354193418641566L; 45 46 /** The numerator degrees of freedom*/ 47 private double numeratorDegreesOfFreedom; 48 49 /** The numerator degrees of freedom*/ 50 private double denominatorDegreesOfFreedom; 51 52 /** Inverse cumulative probability accuracy */ 53 private final double solverAbsoluteAccuracy; 54 55 /** 56 * Create a F distribution using the given degrees of freedom. 57 * @param numeratorDegreesOfFreedom the numerator degrees of freedom. 58 * @param denominatorDegreesOfFreedom the denominator degrees of freedom. 59 */ 60 public FDistributionImpl(double numeratorDegreesOfFreedom, 61 double denominatorDegreesOfFreedom) { 62 this(numeratorDegreesOfFreedom, denominatorDegreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY); 63 } 64 65 /** 66 * Create a F distribution using the given degrees of freedom and inverse cumulative probability accuracy. 67 * @param numeratorDegreesOfFreedom the numerator degrees of freedom. 68 * @param denominatorDegreesOfFreedom the denominator degrees of freedom. 69 * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates 70 * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}) 71 * @since 2.1 72 */ 73 public FDistributionImpl(double numeratorDegreesOfFreedom, double denominatorDegreesOfFreedom, 74 double inverseCumAccuracy) { 75 super(); 76 setNumeratorDegreesOfFreedomInternal(numeratorDegreesOfFreedom); 77 setDenominatorDegreesOfFreedomInternal(denominatorDegreesOfFreedom); 78 solverAbsoluteAccuracy = inverseCumAccuracy; 79 } 80 81 /** 82 * Returns the probability density for a particular point. 83 * 84 * @param x The point at which the density should be computed. 85 * @return The pdf at point x. 86 * @since 2.1 87 */ 88 @Override 89 public double density(double x) { 90 final double nhalf = numeratorDegreesOfFreedom / 2; 91 final double mhalf = denominatorDegreesOfFreedom / 2; 92 final double logx = FastMath.log(x); 93 final double logn = FastMath.log(numeratorDegreesOfFreedom); 94 final double logm = FastMath.log(denominatorDegreesOfFreedom); 95 final double lognxm = FastMath.log(numeratorDegreesOfFreedom * x + denominatorDegreesOfFreedom); 96 return FastMath.exp(nhalf*logn + nhalf*logx - logx + mhalf*logm - nhalf*lognxm - 97 mhalf*lognxm - Beta.logBeta(nhalf, mhalf)); 98 } 99 100 /** 101 * For this distribution, X, this method returns P(X < x). 102 * 103 * The implementation of this method is based on: 104 * <ul> 105 * <li> 106 * <a href="http://mathworld.wolfram.com/F-Distribution.html"> 107 * F-Distribution</a>, equation (4).</li> 108 * </ul> 109 * 110 * @param x the value at which the CDF is evaluated. 111 * @return CDF for this distribution. 112 * @throws MathException if the cumulative probability can not be 113 * computed due to convergence or other numerical errors. 114 */ 115 public double cumulativeProbability(double x) throws MathException { 116 double ret; 117 if (x <= 0.0) { 118 ret = 0.0; 119 } else { 120 double n = numeratorDegreesOfFreedom; 121 double m = denominatorDegreesOfFreedom; 122 123 ret = Beta.regularizedBeta((n * x) / (m + n * x), 124 0.5 * n, 125 0.5 * m); 126 } 127 return ret; 128 } 129 130 /** 131 * For this distribution, X, this method returns the critical point x, such 132 * that P(X < x) = <code>p</code>. 133 * <p> 134 * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p> 135 * 136 * @param p the desired probability 137 * @return x, such that P(X < x) = <code>p</code> 138 * @throws MathException if the inverse cumulative probability can not be 139 * computed due to convergence or other numerical errors. 140 * @throws IllegalArgumentException if <code>p</code> is not a valid 141 * probability. 142 */ 143 @Override 144 public double inverseCumulativeProbability(final double p) 145 throws MathException { 146 if (p == 0) { 147 return 0d; 148 } 149 if (p == 1) { 150 return Double.POSITIVE_INFINITY; 151 } 152 return super.inverseCumulativeProbability(p); 153 } 154 155 /** 156 * Access the domain value lower bound, based on <code>p</code>, used to 157 * bracket a CDF root. This method is used by 158 * {@link #inverseCumulativeProbability(double)} to find critical values. 159 * 160 * @param p the desired probability for the critical value 161 * @return domain value lower bound, i.e. 162 * P(X < <i>lower bound</i>) < <code>p</code> 163 */ 164 @Override 165 protected double getDomainLowerBound(double p) { 166 return 0.0; 167 } 168 169 /** 170 * Access the domain value upper bound, based on <code>p</code>, used to 171 * bracket a CDF root. This method is used by 172 * {@link #inverseCumulativeProbability(double)} to find critical values. 173 * 174 * @param p the desired probability for the critical value 175 * @return domain value upper bound, i.e. 176 * P(X < <i>upper bound</i>) > <code>p</code> 177 */ 178 @Override 179 protected double getDomainUpperBound(double p) { 180 return Double.MAX_VALUE; 181 } 182 183 /** 184 * Access the initial domain value, based on <code>p</code>, used to 185 * bracket a CDF root. This method is used by 186 * {@link #inverseCumulativeProbability(double)} to find critical values. 187 * 188 * @param p the desired probability for the critical value 189 * @return initial domain value 190 */ 191 @Override 192 protected double getInitialDomain(double p) { 193 double ret = 1.0; 194 double d = denominatorDegreesOfFreedom; 195 if (d > 2.0) { 196 // use mean 197 ret = d / (d - 2.0); 198 } 199 return ret; 200 } 201 202 /** 203 * Modify the numerator degrees of freedom. 204 * @param degreesOfFreedom the new numerator degrees of freedom. 205 * @throws IllegalArgumentException if <code>degreesOfFreedom</code> is not 206 * positive. 207 * @deprecated as of 2.1 (class will become immutable in 3.0) 208 */ 209 @Deprecated 210 public void setNumeratorDegreesOfFreedom(double degreesOfFreedom) { 211 setNumeratorDegreesOfFreedomInternal(degreesOfFreedom); 212 } 213 214 /** 215 * Modify the numerator degrees of freedom. 216 * @param degreesOfFreedom the new numerator degrees of freedom. 217 * @throws IllegalArgumentException if <code>degreesOfFreedom</code> is not 218 * positive. 219 */ 220 private void setNumeratorDegreesOfFreedomInternal(double degreesOfFreedom) { 221 if (degreesOfFreedom <= 0.0) { 222 throw MathRuntimeException.createIllegalArgumentException( 223 LocalizedFormats.NOT_POSITIVE_DEGREES_OF_FREEDOM, degreesOfFreedom); 224 } 225 this.numeratorDegreesOfFreedom = degreesOfFreedom; 226 } 227 228 /** 229 * Access the numerator degrees of freedom. 230 * @return the numerator degrees of freedom. 231 */ 232 public double getNumeratorDegreesOfFreedom() { 233 return numeratorDegreesOfFreedom; 234 } 235 236 /** 237 * Modify the denominator degrees of freedom. 238 * @param degreesOfFreedom the new denominator degrees of freedom. 239 * @throws IllegalArgumentException if <code>degreesOfFreedom</code> is not 240 * positive. 241 * @deprecated as of 2.1 (class will become immutable in 3.0) 242 */ 243 @Deprecated 244 public void setDenominatorDegreesOfFreedom(double degreesOfFreedom) { 245 setDenominatorDegreesOfFreedomInternal(degreesOfFreedom); 246 } 247 248 /** 249 * Modify the denominator degrees of freedom. 250 * @param degreesOfFreedom the new denominator degrees of freedom. 251 * @throws IllegalArgumentException if <code>degreesOfFreedom</code> is not 252 * positive. 253 */ 254 private void setDenominatorDegreesOfFreedomInternal(double degreesOfFreedom) { 255 if (degreesOfFreedom <= 0.0) { 256 throw MathRuntimeException.createIllegalArgumentException( 257 LocalizedFormats.NOT_POSITIVE_DEGREES_OF_FREEDOM, degreesOfFreedom); 258 } 259 this.denominatorDegreesOfFreedom = degreesOfFreedom; 260 } 261 262 /** 263 * Access the denominator degrees of freedom. 264 * @return the denominator degrees of freedom. 265 */ 266 public double getDenominatorDegreesOfFreedom() { 267 return denominatorDegreesOfFreedom; 268 } 269 270 /** 271 * Return the absolute accuracy setting of the solver used to estimate 272 * inverse cumulative probabilities. 273 * 274 * @return the solver absolute accuracy 275 * @since 2.1 276 */ 277 @Override 278 protected double getSolverAbsoluteAccuracy() { 279 return solverAbsoluteAccuracy; 280 } 281 282 /** 283 * Returns the lower bound of the support for the distribution. 284 * 285 * The lower bound of the support is always 0, regardless of the parameters. 286 * 287 * @return lower bound of the support (always 0) 288 * @since 2.2 289 */ 290 public double getSupportLowerBound() { 291 return 0; 292 } 293 294 /** 295 * Returns the upper bound of the support for the distribution. 296 * 297 * The upper bound of the support is always positive infinity, 298 * regardless of the parameters. 299 * 300 * @return upper bound of the support (always Double.POSITIVE_INFINITY) 301 * @since 2.2 302 */ 303 public double getSupportUpperBound() { 304 return Double.POSITIVE_INFINITY; 305 } 306 307 /** 308 * Returns the mean of the distribution. 309 * 310 * For denominator degrees of freedom parameter <code>b</code>, 311 * the mean is 312 * <ul> 313 * <li>if <code>b > 2</code> then <code>b / (b - 2)</code></li> 314 * <li>else <code>undefined</code> 315 * </ul> 316 * 317 * @return the mean 318 * @since 2.2 319 */ 320 public double getNumericalMean() { 321 final double denominatorDF = getDenominatorDegreesOfFreedom(); 322 323 if (denominatorDF > 2) { 324 return denominatorDF / (denominatorDF - 2); 325 } 326 327 return Double.NaN; 328 } 329 330 /** 331 * Returns the variance of the distribution. 332 * 333 * For numerator degrees of freedom parameter <code>a</code> 334 * and denominator degrees of freedom parameter <code>b</code>, 335 * the variance is 336 * <ul> 337 * <li> 338 * if <code>b > 4</code> then 339 * <code>[ 2 * b^2 * (a + b - 2) ] / [ a * (b - 2)^2 * (b - 4) ]</code> 340 * </li> 341 * <li>else <code>undefined</code> 342 * </ul> 343 * 344 * @return the variance 345 * @since 2.2 346 */ 347 public double getNumericalVariance() { 348 final double denominatorDF = getDenominatorDegreesOfFreedom(); 349 350 if (denominatorDF > 4) { 351 final double numeratorDF = getNumeratorDegreesOfFreedom(); 352 final double denomDFMinusTwo = denominatorDF - 2; 353 354 return ( 2 * (denominatorDF * denominatorDF) * (numeratorDF + denominatorDF - 2) ) / 355 ( (numeratorDF * (denomDFMinusTwo * denomDFMinusTwo) * (denominatorDF - 4)) ); 356 } 357 358 return Double.NaN; 359 } 360 } 361
