| /* |
| * 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; |
| } |
| } |