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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.math3.distribution;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.apache.commons.math3.util.FastMath;
/**
* Implementation of the Cauchy distribution.
*
* @see Cauchy distribution (Wikipedia)
* @see Cauchy Distribution (MathWorld)
* @since 1.1 (changed to concrete class in 3.0)
*/
public class CauchyDistribution extends AbstractRealDistribution {
/**
* 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 a Cauchy distribution with the median equal to zero and scale
* equal to one.
*/
public CauchyDistribution() {
this(0, 1);
}
/**
* Creates a Cauchy distribution using the given median and scale.
*
* Note: this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @param median Median for this distribution.
* @param scale Scale parameter for this distribution.
*/
public CauchyDistribution(double median, double scale) {
this(median, scale, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Creates a Cauchy distribution using the given median and scale.
*
* Note: this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @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 scale <= 0}.
* @since 2.1
*/
public CauchyDistribution(double median, double scale,
double inverseCumAccuracy) {
this(new Well19937c(), median, scale, inverseCumAccuracy);
}
/**
* Creates a Cauchy distribution.
*
* @param rng Random number generator.
* @param median Median for this distribution.
* @param scale Scale parameter for this distribution.
* @throws NotStrictlyPositiveException if {@code scale <= 0}.
* @since 3.3
*/
public CauchyDistribution(RandomGenerator rng, double median, double scale) {
this(rng, median, scale, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Creates a Cauchy distribution.
*
* @param rng Random number generator.
* @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 scale <= 0}.
* @since 3.1
*/
public CauchyDistribution(RandomGenerator rng,
double median,
double scale,
double inverseCumAccuracy) {
super(rng);
if (scale <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
}
this.scale = scale;
this.median = median;
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/** {@inheritDoc} */
public double cumulativeProbability(double x) {
return 0.5 + (FastMath.atan((x - median) / scale) / FastMath.PI);
}
/**
* Access the median.
*
* @return the median for this distribution.
*/
public double getMedian() {
return median;
}
/**
* Access the scale parameter.
*
* @return the scale parameter for this distribution.
*/
public double getScale() {
return scale;
}
/** {@inheritDoc} */
public double density(double x) {
final double dev = x - median;
return (1 / FastMath.PI) * (scale / (dev * dev + scale * scale));
}
/**
* {@inheritDoc}
*
* Returns {@code Double.NEGATIVE_INFINITY} when {@code p == 0}
* and {@code Double.POSITIVE_INFINITY} when {@code p == 1}.
*/
@Override
public double inverseCumulativeProbability(double p) throws OutOfRangeException {
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;
}
/** {@inheritDoc} */
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* {@inheritDoc}
*
* The mean is always undefined no matter the parameters.
*
* @return mean (always Double.NaN)
*/
public double getNumericalMean() {
return Double.NaN;
}
/**
* {@inheritDoc}
*
* The variance is always undefined no matter the parameters.
*
* @return variance (always Double.NaN)
*/
public double getNumericalVariance() {
return Double.NaN;
}
/**
* {@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)
*/
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)
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/** {@inheritDoc} */
public boolean isSupportLowerBoundInclusive() {
return false;
}
/** {@inheritDoc} */
public boolean isSupportUpperBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
}