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.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 | } |