Java tutorial
/* * 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; } }