/* * 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.special.Beta; import org.apache.commons.math.special.Gamma; /** * Default implementation of * {@link org.apache.commons.math.distribution.TDistribution}. * * @version $Revision: 925812 $ $Date: 2010-03-21 11:49:31 -0400 (Sun, 21 Mar 2010) $ */ 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) */ @Override @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( "degrees of freedom must be positive ({0})", newDegreesOfFreedom); } this.degreesOfFreedom = newDegreesOfFreedom; } /** * Access the degrees of freedom. * * @return the degrees of freedom. */ @Override 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 plus1Over2 = (n + 1) / 2; return Math.exp(Gamma.logGamma(plus1Over2) - 0.5 * (Math.log(Math.PI) + Math.log(n)) - Gamma.logGamma(n / 2) - plus1Over2 * Math.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 evaluted at <code>x</code>. * @throws MathException if the cumulative probability can not be * computed due to convergence or other numerical errors. */ @Override 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; } }