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/*
* 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;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.util.FastMath;
/**
* Default implementation of
* {@link org.apache.commons.math.distribution.CauchyDistribution}.
*
* @since 1.1
* @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
*/
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 < x).
* @param x the value at which the CDF is evaluated.
* @return CDF evaluated at x.
*/
public double cumulativeProbability(double x) {
return 0.5 + (FastMath.atan((x - median) / scale) / FastMath.PI);
}
/**
* Access the median.
* @return median for this distribution
*/
public double getMedian() {
return median;
}
/**
* Access the scale parameter.
* @return scale parameter for this distribution
*/
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 / FastMath.PI) * (scale / (dev * dev + scale * scale));
}
/**
* 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 IllegalArgumentException if p is not a valid
* probability.
*/
@Override
public double inverseCumulativeProbability(double p) {
double ret;
if (p < 0.0 || p > 1.0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.OUT_OF_RANGE_SIMPLE, 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 * FastMath.tan(FastMath.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)
*/
@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 sd is not positive.
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setScale(double s) {
setScaleInternal(s);
}
/**
* Modify the scale parameter.
* @param s scale parameter for this distribution
* @throws IllegalArgumentException if sd is not positive.
*/
private void setScaleInternal(double s) {
if (s <= 0.0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.NOT_POSITIVE_SCALE, s);
}
scale = s;
}
/**
* 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) {
double ret;
if (p < .5) {
ret = -Double.MAX_VALUE;
} else {
ret = median;
}
return ret;
}
/**
* 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) {
double ret;
if (p < .5) {
ret = median;
} else {
ret = Double.MAX_VALUE;
}
return ret;
}
/**
* 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) {
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;
}
/**
* Returns the lower bound of the support for this distribution.
* The lower bound of the support of the Cauchy distribution is always
* negative infinity, regardless of 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 this distribution.
* The upper bound of the support of the Cauchy distribution is always
* positive infinity, regardless of 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.
*
* The mean is always undefined, regardless of the parameters.
*
* @return mean (always Double.NaN)
* @since 2.2
*/
public double getNumericalMean() {
return Double.NaN;
}
/**
* Returns the variance.
*
* The variance is always undefined, regardless of the parameters.
*
* @return variance (always Double.NaN)
* @since 2.2
*/
public double getNumericalVariance() {
return Double.NaN;
}
}
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