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