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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 < <code>x</code>). * @param x the value at which the CDF is evaluated. * @return CDF evaluated at <code>x</code>. */ 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) = <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(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 <code>sd</code> 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 <code>sd</code> 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 <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; } /** * 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; } }