Java tutorial
/* * 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.MathException; import org.apache.commons.math.MathRuntimeException; import org.apache.commons.math.exception.util.LocalizedFormats; import org.apache.commons.math.special.Erf; import org.apache.commons.math.util.FastMath; /** * Default implementation of * {@link org.apache.commons.math.distribution.NormalDistribution}. * * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $ */ public class NormalDistributionImpl extends AbstractContinuousDistribution implements NormalDistribution, 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; /** &sqrt;(2 π) */ private static final double SQRT2PI = FastMath.sqrt(2 * FastMath.PI); /** The mean of this distribution. */ private double mean = 0; /** The standard deviation of this distribution. */ private double standardDeviation = 1; /** Inverse cumulative probability accuracy */ private final double solverAbsoluteAccuracy; /** * Create a normal distribution using the given mean and standard deviation. * @param mean mean for this distribution * @param sd standard deviation for this distribution */ public NormalDistributionImpl(double mean, double sd) { this(mean, sd, DEFAULT_INVERSE_ABSOLUTE_ACCURACY); } /** * Create a normal distribution using the given mean, standard deviation and * inverse cumulative distribution accuracy. * * @param mean mean for this distribution * @param sd standard deviation for this distribution * @param inverseCumAccuracy inverse cumulative probability accuracy * @since 2.1 */ public NormalDistributionImpl(double mean, double sd, double inverseCumAccuracy) { super(); setMeanInternal(mean); setStandardDeviationInternal(sd); solverAbsoluteAccuracy = inverseCumAccuracy; } /** * Creates normal distribution with the mean equal to zero and standard * deviation equal to one. */ public NormalDistributionImpl() { this(0.0, 1.0); } /** * Access the mean. * @return mean for this distribution */ public double getMean() { return mean; } /** * Modify the mean. * @param mean for this distribution * @deprecated as of 2.1 (class will become immutable in 3.0) */ @Deprecated public void setMean(double mean) { setMeanInternal(mean); } /** * Modify the mean. * @param newMean for this distribution */ private void setMeanInternal(double newMean) { this.mean = newMean; } /** * Access the standard deviation. * @return standard deviation for this distribution */ public double getStandardDeviation() { return standardDeviation; } /** * Modify the standard deviation. * @param sd standard deviation 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 setStandardDeviation(double sd) { setStandardDeviationInternal(sd); } /** * Modify the standard deviation. * @param sd standard deviation for this distribution * @throws IllegalArgumentException if <code>sd</code> is not positive. */ private void setStandardDeviationInternal(double sd) { if (sd <= 0.0) { throw MathRuntimeException .createIllegalArgumentException(LocalizedFormats.NOT_POSITIVE_STANDARD_DEVIATION, sd); } standardDeviation = sd; } /** * Return the probability density for a particular point. * * @param x The point at which the density should be computed. * @return The pdf at point x. * @deprecated */ @Deprecated public double density(Double x) { return density(x.doubleValue()); } /** * 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) { double x0 = x - mean; return FastMath.exp(-x0 * x0 / (2 * standardDeviation * standardDeviation)) / (standardDeviation * SQRT2PI); } /** * For this distribution, X, this method returns P(X < <code>x</code>). * If <code>x</code>is more than 40 standard deviations from the mean, 0 or 1 is returned, * as in these cases the actual value is within <code>Double.MIN_VALUE</code> of 0 or 1. * * @param x the value at which the CDF is evaluated. * @return CDF evaluated at <code>x</code>. * @throws MathException if the algorithm fails to converge */ public double cumulativeProbability(double x) throws MathException { final double dev = x - mean; if (FastMath.abs(dev) > 40 * standardDeviation) { return dev < 0 ? 0.0d : 1.0d; } return 0.5 * (1.0 + Erf.erf(dev / (standardDeviation * FastMath.sqrt(2.0)))); } /** * 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; } /** * 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 MathException if the inverse cumulative probability can not be * computed due to convergence or other numerical errors. * @throws IllegalArgumentException if <code>p</code> is not a valid * probability. */ @Override public double inverseCumulativeProbability(final double p) throws MathException { if (p == 0) { return Double.NEGATIVE_INFINITY; } if (p == 1) { return Double.POSITIVE_INFINITY; } return super.inverseCumulativeProbability(p); } /** * Generates a random value sampled from this distribution. * * @return random value * @since 2.2 * @throws MathException if an error occurs generating the random value */ @Override public double sample() throws MathException { return randomData.nextGaussian(mean, standardDeviation); } /** * 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 = mean; } 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 = mean; } 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 = mean - standardDeviation; } else if (p > .5) { ret = mean + standardDeviation; } else { ret = mean; } return ret; } /** * Returns the lower bound of the support for the distribution. * * The lower bound of the support is always negative infinity * no matter 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 the distribution. * * The upper bound of the support is always positive infinity * no matter the parameters. * * @return upper bound of the support (always Double.POSITIVE_INFINITY) * @since 2.2 */ public double getSupportUpperBound() { return Double.POSITIVE_INFINITY; } /** * Returns the variance. * * For standard deviation parameter <code>s</code>, * the variance is <code>s^2</code> * * @return the variance * @since 2.2 */ public double getNumericalVariance() { final double s = getStandardDeviation(); return s * s; } }