/*
* 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;
}
}