| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.math.distribution; |
| |
| import java.io.Serializable; |
| |
| import org.apache.commons.math.MathException; |
| import org.apache.commons.math.MathRuntimeException; |
| import org.apache.commons.math.exception.util.LocalizedFormats; |
| import org.apache.commons.math.special.Beta; |
| import org.apache.commons.math.util.FastMath; |
| |
| /** |
| * Default implementation of |
| * {@link org.apache.commons.math.distribution.FDistribution}. |
| * |
| * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $ |
| */ |
| public class FDistributionImpl |
| extends AbstractContinuousDistribution |
| implements FDistribution, Serializable { |
| |
| /** |
| * Default inverse cumulative probability accuracy |
| * @since 2.1 |
| */ |
| public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9; |
| |
| /** Serializable version identifier */ |
| private static final long serialVersionUID = -8516354193418641566L; |
| |
| /** The numerator degrees of freedom*/ |
| private double numeratorDegreesOfFreedom; |
| |
| /** The numerator degrees of freedom*/ |
| private double denominatorDegreesOfFreedom; |
| |
| /** Inverse cumulative probability accuracy */ |
| private final double solverAbsoluteAccuracy; |
| |
| /** |
| * Create a F distribution using the given degrees of freedom. |
| * @param numeratorDegreesOfFreedom the numerator degrees of freedom. |
| * @param denominatorDegreesOfFreedom the denominator degrees of freedom. |
| */ |
| public FDistributionImpl(double numeratorDegreesOfFreedom, |
| double denominatorDegreesOfFreedom) { |
| this(numeratorDegreesOfFreedom, denominatorDegreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY); |
| } |
| |
| /** |
| * Create a F distribution using the given degrees of freedom and inverse cumulative probability accuracy. |
| * @param numeratorDegreesOfFreedom the numerator degrees of freedom. |
| * @param denominatorDegreesOfFreedom the denominator degrees of freedom. |
| * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates |
| * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}) |
| * @since 2.1 |
| */ |
| public FDistributionImpl(double numeratorDegreesOfFreedom, double denominatorDegreesOfFreedom, |
| double inverseCumAccuracy) { |
| super(); |
| setNumeratorDegreesOfFreedomInternal(numeratorDegreesOfFreedom); |
| setDenominatorDegreesOfFreedomInternal(denominatorDegreesOfFreedom); |
| solverAbsoluteAccuracy = inverseCumAccuracy; |
| } |
| |
| /** |
| * Returns the probability density for a particular point. |
| * |
| * @param x The point at which the density should be computed. |
| * @return The pdf at point x. |
| * @since 2.1 |
| */ |
| @Override |
| public double density(double x) { |
| final double nhalf = numeratorDegreesOfFreedom / 2; |
| final double mhalf = denominatorDegreesOfFreedom / 2; |
| final double logx = FastMath.log(x); |
| final double logn = FastMath.log(numeratorDegreesOfFreedom); |
| final double logm = FastMath.log(denominatorDegreesOfFreedom); |
| final double lognxm = FastMath.log(numeratorDegreesOfFreedom * x + denominatorDegreesOfFreedom); |
| return FastMath.exp(nhalf*logn + nhalf*logx - logx + mhalf*logm - nhalf*lognxm - |
| mhalf*lognxm - Beta.logBeta(nhalf, mhalf)); |
| } |
| |
| /** |
| * For this distribution, X, this method returns P(X < x). |
| * |
| * The implementation of this method is based on: |
| * <ul> |
| * <li> |
| * <a href="http://mathworld.wolfram.com/F-Distribution.html"> |
| * F-Distribution</a>, equation (4).</li> |
| * </ul> |
| * |
| * @param x the value at which the CDF is evaluated. |
| * @return CDF for this distribution. |
| * @throws MathException if the cumulative probability can not be |
| * computed due to convergence or other numerical errors. |
| */ |
| public double cumulativeProbability(double x) throws MathException { |
| double ret; |
| if (x <= 0.0) { |
| ret = 0.0; |
| } else { |
| double n = numeratorDegreesOfFreedom; |
| double m = denominatorDegreesOfFreedom; |
| |
| ret = Beta.regularizedBeta((n * x) / (m + n * x), |
| 0.5 * n, |
| 0.5 * m); |
| } |
| return ret; |
| } |
| |
| /** |
| * For this distribution, X, this method returns the critical point x, such |
| * that P(X < x) = <code>p</code>. |
| * <p> |
| * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p> |
| * |
| * @param p the desired probability |
| * @return x, such that P(X < x) = <code>p</code> |
| * @throws MathException if the inverse cumulative probability can not be |
| * computed due to convergence or other numerical errors. |
| * @throws IllegalArgumentException if <code>p</code> is not a valid |
| * probability. |
| */ |
| @Override |
| public double inverseCumulativeProbability(final double p) |
| throws MathException { |
| if (p == 0) { |
| return 0d; |
| } |
| if (p == 1) { |
| return Double.POSITIVE_INFINITY; |
| } |
| return super.inverseCumulativeProbability(p); |
| } |
| |
| /** |
| * Access the domain value lower bound, based on <code>p</code>, used to |
| * bracket a CDF root. This method is used by |
| * {@link #inverseCumulativeProbability(double)} to find critical values. |
| * |
| * @param p the desired probability for the critical value |
| * @return domain value lower bound, i.e. |
| * P(X < <i>lower bound</i>) < <code>p</code> |
| */ |
| @Override |
| protected double getDomainLowerBound(double p) { |
| return 0.0; |
| } |
| |
| /** |
| * Access the domain value upper bound, based on <code>p</code>, used to |
| * bracket a CDF root. This method is used by |
| * {@link #inverseCumulativeProbability(double)} to find critical values. |
| * |
| * @param p the desired probability for the critical value |
| * @return domain value upper bound, i.e. |
| * P(X < <i>upper bound</i>) > <code>p</code> |
| */ |
| @Override |
| protected double getDomainUpperBound(double p) { |
| return Double.MAX_VALUE; |
| } |
| |
| /** |
| * Access the initial domain value, based on <code>p</code>, used to |
| * bracket a CDF root. This method is used by |
| * {@link #inverseCumulativeProbability(double)} to find critical values. |
| * |
| * @param p the desired probability for the critical value |
| * @return initial domain value |
| */ |
| @Override |
| protected double getInitialDomain(double p) { |
| double ret = 1.0; |
| double d = denominatorDegreesOfFreedom; |
| if (d > 2.0) { |
| // use mean |
| ret = d / (d - 2.0); |
| } |
| return ret; |
| } |
| |
| /** |
| * Modify the numerator degrees of freedom. |
| * @param degreesOfFreedom the new numerator degrees of freedom. |
| * @throws IllegalArgumentException if <code>degreesOfFreedom</code> is not |
| * positive. |
| * @deprecated as of 2.1 (class will become immutable in 3.0) |
| */ |
| @Deprecated |
| public void setNumeratorDegreesOfFreedom(double degreesOfFreedom) { |
| setNumeratorDegreesOfFreedomInternal(degreesOfFreedom); |
| } |
| |
| /** |
| * Modify the numerator degrees of freedom. |
| * @param degreesOfFreedom the new numerator degrees of freedom. |
| * @throws IllegalArgumentException if <code>degreesOfFreedom</code> is not |
| * positive. |
| */ |
| private void setNumeratorDegreesOfFreedomInternal(double degreesOfFreedom) { |
| if (degreesOfFreedom <= 0.0) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NOT_POSITIVE_DEGREES_OF_FREEDOM, degreesOfFreedom); |
| } |
| this.numeratorDegreesOfFreedom = degreesOfFreedom; |
| } |
| |
| /** |
| * Access the numerator degrees of freedom. |
| * @return the numerator degrees of freedom. |
| */ |
| public double getNumeratorDegreesOfFreedom() { |
| return numeratorDegreesOfFreedom; |
| } |
| |
| /** |
| * Modify the denominator degrees of freedom. |
| * @param degreesOfFreedom the new denominator degrees of freedom. |
| * @throws IllegalArgumentException if <code>degreesOfFreedom</code> is not |
| * positive. |
| * @deprecated as of 2.1 (class will become immutable in 3.0) |
| */ |
| @Deprecated |
| public void setDenominatorDegreesOfFreedom(double degreesOfFreedom) { |
| setDenominatorDegreesOfFreedomInternal(degreesOfFreedom); |
| } |
| |
| /** |
| * Modify the denominator degrees of freedom. |
| * @param degreesOfFreedom the new denominator degrees of freedom. |
| * @throws IllegalArgumentException if <code>degreesOfFreedom</code> is not |
| * positive. |
| */ |
| private void setDenominatorDegreesOfFreedomInternal(double degreesOfFreedom) { |
| if (degreesOfFreedom <= 0.0) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NOT_POSITIVE_DEGREES_OF_FREEDOM, degreesOfFreedom); |
| } |
| this.denominatorDegreesOfFreedom = degreesOfFreedom; |
| } |
| |
| /** |
| * Access the denominator degrees of freedom. |
| * @return the denominator degrees of freedom. |
| */ |
| public double getDenominatorDegreesOfFreedom() { |
| return denominatorDegreesOfFreedom; |
| } |
| |
| /** |
| * Return the absolute accuracy setting of the solver used to estimate |
| * inverse cumulative probabilities. |
| * |
| * @return the solver absolute accuracy |
| * @since 2.1 |
| */ |
| @Override |
| protected double getSolverAbsoluteAccuracy() { |
| return solverAbsoluteAccuracy; |
| } |
| |
| /** |
| * Returns the lower bound of the support for the distribution. |
| * |
| * The lower bound of the support is always 0, regardless of the parameters. |
| * |
| * @return lower bound of the support (always 0) |
| * @since 2.2 |
| */ |
| public double getSupportLowerBound() { |
| return 0; |
| } |
| |
| /** |
| * Returns the upper bound of the support for the distribution. |
| * |
| * The upper bound of the support is always positive infinity, |
| * regardless of the parameters. |
| * |
| * @return upper bound of the support (always Double.POSITIVE_INFINITY) |
| * @since 2.2 |
| */ |
| public double getSupportUpperBound() { |
| return Double.POSITIVE_INFINITY; |
| } |
| |
| /** |
| * Returns the mean of the distribution. |
| * |
| * For denominator degrees of freedom parameter <code>b</code>, |
| * the mean is |
| * <ul> |
| * <li>if <code>b > 2</code> then <code>b / (b - 2)</code></li> |
| * <li>else <code>undefined</code> |
| * </ul> |
| * |
| * @return the mean |
| * @since 2.2 |
| */ |
| public double getNumericalMean() { |
| final double denominatorDF = getDenominatorDegreesOfFreedom(); |
| |
| if (denominatorDF > 2) { |
| return denominatorDF / (denominatorDF - 2); |
| } |
| |
| return Double.NaN; |
| } |
| |
| /** |
| * Returns the variance of the distribution. |
| * |
| * For numerator degrees of freedom parameter <code>a</code> |
| * and denominator degrees of freedom parameter <code>b</code>, |
| * the variance is |
| * <ul> |
| * <li> |
| * if <code>b > 4</code> then |
| * <code>[ 2 * b^2 * (a + b - 2) ] / [ a * (b - 2)^2 * (b - 4) ]</code> |
| * </li> |
| * <li>else <code>undefined</code> |
| * </ul> |
| * |
| * @return the variance |
| * @since 2.2 |
| */ |
| public double getNumericalVariance() { |
| final double denominatorDF = getDenominatorDegreesOfFreedom(); |
| |
| if (denominatorDF > 4) { |
| final double numeratorDF = getNumeratorDegreesOfFreedom(); |
| final double denomDFMinusTwo = denominatorDF - 2; |
| |
| return ( 2 * (denominatorDF * denominatorDF) * (numeratorDF + denominatorDF - 2) ) / |
| ( (numeratorDF * (denomDFMinusTwo * denomDFMinusTwo) * (denominatorDF - 4)) ); |
| } |
| |
| return Double.NaN; |
| } |
| } |