| /* |
| * 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; |
| } |
| |
| } |