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.special.Gamma; import org.apache.commons.math.util.FastMath; /** * Default implementation of * {@link org.apache.commons.math.distribution.TDistribution}. * * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $ */ public class TDistributionImpl extends AbstractContinuousDistribution implements TDistribution, 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 = -5852615386664158222L; /** The degrees of freedom*/ private double degreesOfFreedom; /** Inverse cumulative probability accuracy */ private final double solverAbsoluteAccuracy; /** * Create a t distribution using the given degrees of freedom and the * specified inverse cumulative probability absolute accuracy. * * @param degreesOfFreedom the 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 TDistributionImpl(double degreesOfFreedom, double inverseCumAccuracy) { super(); setDegreesOfFreedomInternal(degreesOfFreedom); solverAbsoluteAccuracy = inverseCumAccuracy; } /** * Create a t distribution using the given degrees of freedom. * @param degreesOfFreedom the degrees of freedom. */ public TDistributionImpl(double degreesOfFreedom) { this(degreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY); } /** * Modify the degrees of freedom. * @param degreesOfFreedom the new degrees of freedom. * @deprecated as of 2.1 (class will become immutable in 3.0) */ @Deprecated public void setDegreesOfFreedom(double degreesOfFreedom) { setDegreesOfFreedomInternal(degreesOfFreedom); } /** * Modify the degrees of freedom. * @param newDegreesOfFreedom the new degrees of freedom. */ private void setDegreesOfFreedomInternal(double newDegreesOfFreedom) { if (newDegreesOfFreedom <= 0.0) { throw MathRuntimeException.createIllegalArgumentException( LocalizedFormats.NOT_POSITIVE_DEGREES_OF_FREEDOM, newDegreesOfFreedom); } this.degreesOfFreedom = newDegreesOfFreedom; } /** * Access the degrees of freedom. * @return the degrees of freedom. */ public double getDegreesOfFreedom() { return degreesOfFreedom; } /** * 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 n = degreesOfFreedom; final double nPlus1Over2 = (n + 1) / 2; return FastMath.exp(Gamma.logGamma(nPlus1Over2) - 0.5 * (FastMath.log(FastMath.PI) + FastMath.log(n)) - Gamma.logGamma(n / 2) - nPlus1Over2 * FastMath.log(1 + x * x / n)); } /** * For this distribution, X, this method returns P(X < <code>x</code>). * @param x the value at which the CDF is evaluated. * @return CDF evaluated at <code>x</code>. * @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 = 0.5; } else { double t = Beta.regularizedBeta(degreesOfFreedom / (degreesOfFreedom + (x * x)), 0.5 * degreesOfFreedom, 0.5); if (x < 0.0) { ret = 0.5 * t; } else { ret = 1.0 - 0.5 * t; } } return ret; } /** * For this distribution, X, this method returns the critical point x, such * that P(X < x) = <code>p</code>. * <p> * Returns <code>Double.NEGATIVE_INFINITY</code> 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 Double.NEGATIVE_INFINITY; } 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 -Double.MAX_VALUE; } /** * 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) { return 0.0; } /** * 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 negative infinity * no matter the parameters. * * @return lower bound of the support (always Double.NEGATIVE_INFINITY) * @since 2.2 */ public double getSupportLowerBound() { return Double.NEGATIVE_INFINITY; } /** * Returns the upper bound of the support for the distribution. * * The upper bound of the support is always positive infinity * no matter 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. * * For degrees of freedom parameter df, the mean is * <ul> * <li>if <code>df > 1</code> then <code>0</code></li> * <li>else <code>undefined</code></li> * </ul> * * @return the mean * @since 2.2 */ public double getNumericalMean() { final double df = getDegreesOfFreedom(); if (df > 1) { return 0; } return Double.NaN; } /** * Returns the variance. * * For degrees of freedom parameter df, the variance is * <ul> * <li>if <code>df > 2</code> then <code>df / (df - 2)</code> </li> * <li>if <code>1 < df <= 2</code> then <code>positive infinity</code></li> * <li>else <code>undefined</code></li> * </ul> * * @return the variance * @since 2.2 */ public double getNumericalVariance() { final double df = getDegreesOfFreedom(); if (df > 2) { return df / (df - 2); } if (df > 1 && df <= 2) { return Double.POSITIVE_INFINITY; } return Double.NaN; } }