/*
* 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.exception.NotStrictlyPositiveException;
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 $Id: TDistributionImpl.java 1131229 2011-06-03 20:49:25Z luc $
*/
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 final 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 Degrees of freedom.
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code degreesOfFreedom <= 0}
* @since 2.1
*/
public TDistributionImpl(double degreesOfFreedom, double inverseCumAccuracy) {
if (degreesOfFreedom <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.DEGREES_OF_FREEDOM,
degreesOfFreedom);
}
this.degreesOfFreedom = degreesOfFreedom;
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Create a t distribution using the given degrees of freedom.
*
* @param degreesOfFreedom Degrees of freedom.
*/
public TDistributionImpl(double degreesOfFreedom) {
this(degreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Access the degrees of freedom.
*
* @return the degrees of freedom.
*/
public double getDegreesOfFreedom() {
return degreesOfFreedom;
}
/**
* {@inheritDoc}
*/
@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 {@code P(X < x}).
*
* @param x Value at which the CDF is evaluated.
* @return CDF evaluated at {@code x}.
* @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) {
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, {@code X}, this method returns the critical
* point {@code x}, such that {@code P(X < x) = p}.
* Returns {@code Double.NEGATIVE_INFINITY} when p = 0 and
* {@code Double.POSITIVE_INFINITY} when p = 1.
*
* @param p Desired probability.
* @return {@code x}, such that {@code P(X < x) = p}.
* @throws MathException if the inverse cumulative probability cannot be
* computed due to convergence or other numerical errors.
* @throws org.apache.commons.math.exception.OutOfRangeException if
* {@code p} 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}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value
* @return the domain value lower bound, i.e. {@code P(X < 'lower bound') > p}.
*/
@Override
protected double getDomainLowerBound(double p) {
return -Double.MAX_VALUE;
}
/**
* Access the domain value upper bound, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the domain value upper bound, i.e. {@code P(X < 'upper bound') > p}.
*/
@Override
protected double getDomainUpperBound(double p) {
return Double.MAX_VALUE;
}
/**
* Access the initial domain value, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the initial domain value.
*/
@Override
protected double getInitialDomain(double p) {
return 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;
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always negative infinity
* no matter the parameters.
*
* @return lower bound of the support (always Double.NEGATIVE_INFINITY)
*/
@Override
public double getSupportLowerBound() {
return Double.NEGATIVE_INFINITY;
}
/**
* {@inheritDoc}
*
* The upper bound of the support is always positive infinity
* no matter the parameters.
*
* @return upper bound of the support (always Double.POSITIVE_INFINITY)
*/
@Override
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* {@inheritDoc}
*
* 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 {@inheritDoc}
*/
@Override
protected double calculateNumericalMean() {
final double df = getDegreesOfFreedom();
if (df > 1) {
return 0;
}
return Double.NaN;
}
/**
* {@inheritDoc}
*
* 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 {@inheritDoc}
*/
@Override
protected double calculateNumericalVariance() {
final double df = getDegreesOfFreedom();
if (df > 2) {
return df / (df - 2);
}
if (df > 1 && df <= 2) {
return Double.POSITIVE_INFINITY;
}
return Double.NaN;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportLowerBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportUpperBoundInclusive() {
return false;
}
}