/*
* 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.exception.NotStrictlyPositiveException;
import org.apache.commons.math.exception.OutOfRangeException;
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 $Id: CauchyDistributionImpl.java 1131229 2011-06-03 20:49:25Z luc $
*/
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 final double median;
/** The scale of this distribution. */
private final double scale;
/** 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, 1);
}
/**
* Create a cauchy distribution using the given median and scale.
*
* @param median Median for this distribution.
* @param scale Scale parameter for this distribution.
*/
public CauchyDistributionImpl(double median, double scale) {
this(median, scale, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create a cauchy distribution using the given median and scale.
*
* @param median Median for this distribution.
* @param scale Scale parameter for this distribution.
* @param inverseCumAccuracy Maximum absolute error in inverse
* cumulative probability estimates
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code s <= 0}.
* @since 2.1
*/
public CauchyDistributionImpl(double median, double scale,
double inverseCumAccuracy) {
if (scale <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
}
this.scale = scale;
this.median = median;
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* For this distribution, {@code X}, this method returns {@code P(X < x)}.
*
* @param x Value at which the CDF is evaluated.
* @return CDF evaluated at {@code x}.
*/
public double cumulativeProbability(double x) {
return 0.5 + (FastMath.atan((x - median) / scale) / FastMath.PI);
}
/**
* {@inheritDoc}
*/
public double getMedian() {
return median;
}
/**
* {@inheritDoc}
*/
public double getScale() {
return scale;
}
/**
* {@inheritDoc}
*/
@Override
public double density(double x) {
final double dev = x - median;
return (1 / FastMath.PI) * (scale / (dev * dev + scale * scale));
}
/**
* For this distribution, {@code X}, this method returns the critical
* point {@code x}, such that {@code P(X < x) = p}.
* It will return {@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 OutOfRangeException if {@code p} is not a valid probability.
*/
@Override
public double inverseCumulativeProbability(double p) {
double ret;
if (p < 0 || p > 1) {
throw new OutOfRangeException(p, 0, 1);
} 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;
}
/**
* 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 domain value lower bound, i.e. {@code P(X < 'lower bound') < p}.
*/
@Override
protected double getDomainLowerBound(double p) {
double ret;
if (p < 0.5) {
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 Desired probability for the critical value.
* @return domain value lower bound, i.e. {@code P(X < 'upper bound') > p}.
*/
@Override
protected double getDomainUpperBound(double p) {
double ret;
if (p < 0.5) {
ret = median;
} else {
ret = Double.MAX_VALUE;
}
return ret;
}
/**
* 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) {
double ret;
if (p < 0.5) {
ret = median - scale;
} else if (p > 0.5) {
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;
}
/**
* {@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}
*
* The mean is always undefined no matter the parameters.
*
* @return mean (always Double.NaN)
*/
@Override
protected double calculateNumericalMean() {
return Double.NaN;
}
/**
* {@inheritDoc}
*
* The variance is always undefined no matter the parameters.
*
* @return variance (always Double.NaN)
*/
@Override
protected double calculateNumericalVariance() {
return Double.NaN;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportLowerBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportUpperBoundInclusive() {
return false;
}
}