org.apache.commons.math.distribution.TDistributionImpl Maven / Gradle / Ivy
/*
* 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 < x).
* @param x the value at which the CDF is evaluated.
* @return CDF evaluated at 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 == 0.0) {
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) = p.
*
* Returns Double.NEGATIVE_INFINITY for p=0 and
* Double.POSITIVE_INFINITY for p=1.
*
* @param p the desired probability
* @return x, such that P(X < x) = p
* @throws MathException if the inverse cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if 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 p, 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 < lower bound) < p
*/
@Override
protected double getDomainLowerBound(double p) {
return -Double.MAX_VALUE;
}
/**
* Access the domain value upper bound, based on p, 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 < upper bound) > p
*/
@Override
protected double getDomainUpperBound(double p) {
return Double.MAX_VALUE;
}
/**
* Access the initial domain value, based on p, 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
*
* - if
df > 1 then 0
* - else
undefined
*
*
* @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
*
* - if
df > 2 then df / (df - 2)
* - if
1 < df <= 2 then positive infinity
* - else
undefined
*
*
* @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;
}
}