/*
* 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.MathRuntimeException;
/**
* Default implementation of
* {@link org.apache.commons.math.distribution.CauchyDistribution}.
*
* @version $Revision: 925900 $ $Date: 2010-03-21 17:10:07 -0400 (Sun, 21 Mar 2010) $
* @since 1.1
*/
public class CauchyDistributionImpl extends AbstractContinuousDistribution
implements CauchyDistribution, 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 = 8589540077390120676L;
/**
* The median of this distribution.
*/
private double median = 0;
/**
* The scale of this distribution.
*/
private double scale = 1;
/**
* Inverse cumulative probability accuracy
*/
private final double solverAbsoluteAccuracy;
/**
* Creates cauchy distribution with the medain equal to zero and scale
* equal to one.
*/
public CauchyDistributionImpl() {
this(0.0, 1.0);
}
/**
* Create a cauchy distribution using the given median and scale.
*
* @param median median for this distribution
* @param s scale parameter for this distribution
*/
public CauchyDistributionImpl(double median, double s) {
this(median, s, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create a cauchy distribution using the given median and scale.
*
* @param median median for this distribution
* @param s scale parameter for this distribution
* @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
* @since 2.1
*/
public CauchyDistributionImpl(double median, double s, double inverseCumAccuracy) {
super();
setMedianInternal(median);
setScaleInternal(s);
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* 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>.
*/
@Override
public double cumulativeProbability(double x) {
return 0.5 + (Math.atan((x - median) / scale) / Math.PI);
}
/**
* Access the median.
*
* @return median for this distribution
*/
@Override
public double getMedian() {
return median;
}
/**
* Access the scale parameter.
*
* @return scale parameter for this distribution
*/
@Override
public double getScale() {
return scale;
}
/**
* 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 dev = x - median;
return (1 / Math.PI) * (scale / (dev * dev + scale * scale));
}
/**
* 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 IllegalArgumentException if <code>p</code> is not a valid
* probability.
*/
@Override
public double inverseCumulativeProbability(double p) {
double ret;
if (p < 0.0 || p > 1.0) {
throw MathRuntimeException.createIllegalArgumentException(
"{0} out of [{1}, {2}] range", p, 0.0, 1.0);
} else if (p == 0) {
ret = Double.NEGATIVE_INFINITY;
} else if (p == 1) {
ret = Double.POSITIVE_INFINITY;
} else {
ret = median + scale * Math.tan(Math.PI * (p - .5));
}
return ret;
}
/**
* Modify the median.
*
* @param median for this distribution
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Override
@Deprecated
public void setMedian(double median) {
setMedianInternal(median);
}
/**
* Modify the median.
*
* @param newMedian for this distribution
*/
private void setMedianInternal(double newMedian) {
this.median = newMedian;
}
/**
* Modify the scale parameter.
*
* @param s scale parameter for this distribution
* @throws IllegalArgumentException if <code>sd</code> is not positive.
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Override
@Deprecated
public void setScale(double s) {
setScaleInternal(s);
}
/**
* Modify the scale parameter.
*
* @param s scale parameter for this distribution
* @throws IllegalArgumentException if <code>sd</code> is not positive.
*/
private void setScaleInternal(double s) {
if (s <= 0.0) {
throw MathRuntimeException.createIllegalArgumentException(
"scale must be positive ({0})", s);
}
scale = s;
}
/**
* 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) {
double ret;
if (p < .5) {
ret = -Double.MAX_VALUE;
} else {
ret = median;
}
return ret;
}
/**
* 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) {
double ret;
if (p < .5) {
ret = median;
} else {
ret = Double.MAX_VALUE;
}
return ret;
}
/**
* 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) {
double ret;
if (p < .5) {
ret = median - scale;
} else if (p > .5) {
ret = median + scale;
} else {
ret = median;
}
return ret;
}
/**
* 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;
}
}