/*
* 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;
}
}