/*
* 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.math3.distribution;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.special.Erf;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
/**
* Implementation of the normal (gaussian) distribution.
*
* @see <a href="http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution (Wikipedia)</a>
* @see <a href="http://mathworld.wolfram.com/NormalDistribution.html">Normal distribution (MathWorld)</a>
*/
public class NormalDistribution extends AbstractRealDistribution {
/**
* 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;
/** √(2) */
private static final double SQRT2 = FastMath.sqrt(2.0);
/** Mean of this distribution. */
private final double mean;
/** Standard deviation of this distribution. */
private final double standardDeviation;
/** The value of {@code log(sd) + 0.5*log(2*pi)} stored for faster computation. */
private final double logStandardDeviationPlusHalfLog2Pi;
/** Inverse cumulative probability accuracy. */
private final double solverAbsoluteAccuracy;
/**
* Create a normal distribution with mean equal to zero and standard
* deviation equal to one.
*/
public NormalDistribution() {
this(0, 1);
}
/**
* Create a normal distribution using the given mean and standard deviation.
*
* @param mean Mean for this distribution.
* @param sd Standard deviation for this distribution.
* @throws NotStrictlyPositiveException if {@code sd <= 0}.
*/
public NormalDistribution(double mean, double sd)
throws NotStrictlyPositiveException {
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.
* @throws NotStrictlyPositiveException if {@code sd <= 0}.
* @since 2.1
*/
public NormalDistribution(double mean, double sd, double inverseCumAccuracy)
throws NotStrictlyPositiveException {
this(new Well19937c(), mean, sd, inverseCumAccuracy);
}
/**
* Creates a normal distribution.
*
* @param rng Random number generator.
* @param mean Mean for this distribution.
* @param sd Standard deviation for this distribution.
* @throws NotStrictlyPositiveException if {@code sd <= 0}.
* @since 3.3
*/
public NormalDistribution(RandomGenerator rng, double mean, double sd)
throws NotStrictlyPositiveException {
this(rng, mean, sd, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Creates a normal distribution.
*
* @param rng Random number generator.
* @param mean Mean for this distribution.
* @param sd Standard deviation for this distribution.
* @param inverseCumAccuracy Inverse cumulative probability accuracy.
* @throws NotStrictlyPositiveException if {@code sd <= 0}.
* @since 3.1
*/
public NormalDistribution(RandomGenerator rng,
double mean,
double sd,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
if (sd <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.STANDARD_DEVIATION, sd);
}
this.mean = mean;
standardDeviation = sd;
logStandardDeviationPlusHalfLog2Pi = FastMath.log(sd) + 0.5 * FastMath.log(2 * FastMath.PI);
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Access the mean.
*
* @return the mean for this distribution.
*/
public double getMean() {
return mean;
}
/**
* Access the standard deviation.
*
* @return the standard deviation for this distribution.
*/
public double getStandardDeviation() {
return standardDeviation;
}
/** {@inheritDoc} */
public double density(double x) {
return FastMath.exp(logDensity(x));
}
/** {@inheritDoc} */
@Override
public double logDensity(double x) {
final double x0 = x - mean;
final double x1 = x0 / standardDeviation;
return -0.5 * x1 * x1 - logStandardDeviationPlusHalfLog2Pi;
}
/**
* {@inheritDoc}
*
* If {@code x} 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} of 0 or 1.
*/
public double cumulativeProbability(double x) {
final double dev = x - mean;
if (FastMath.abs(dev) > 40 * standardDeviation) {
return dev < 0 ? 0.0d : 1.0d;
}
return 0.5 * (1 + Erf.erf(dev / (standardDeviation * SQRT2)));
}
/** {@inheritDoc}
* @since 3.2
*/
@Override
public double inverseCumulativeProbability(final double p) throws OutOfRangeException {
if (p < 0.0 || p > 1.0) {
throw new OutOfRangeException(p, 0, 1);
}
return mean + standardDeviation * SQRT2 * Erf.erfInv(2 * p - 1);
}
/**
* {@inheritDoc}
*
* @deprecated See {@link RealDistribution#cumulativeProbability(double,double)}
*/
@Override@Deprecated
public double cumulativeProbability(double x0, double x1)
throws NumberIsTooLargeException {
return probability(x0, x1);
}
/** {@inheritDoc} */
@Override
public double probability(double x0,
double x1)
throws NumberIsTooLargeException {
if (x0 > x1) {
throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
x0, x1, true);
}
final double denom = standardDeviation * SQRT2;
final double v0 = (x0 - mean) / denom;
final double v1 = (x1 - mean) / denom;
return 0.5 * Erf.erf(v0, v1);
}
/** {@inheritDoc} */
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* {@inheritDoc}
*
* For mean parameter {@code mu}, the mean is {@code mu}.
*/
public double getNumericalMean() {
return getMean();
}
/**
* {@inheritDoc}
*
* For standard deviation parameter {@code s}, the variance is {@code s^2}.
*/
public double getNumericalVariance() {
final double s = getStandardDeviation();
return s * s;
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always negative infinity
* no matter the parameters.
*
* @return lower bound of the support (always
* {@code Double.NEGATIVE_INFINITY})
*/
public double getSupportLowerBound() {
return Double.NEGATIVE_INFINITY;
}
/**
* {@inheritDoc}
*
* The upper bound of the support is always positive infinity
* no matter the parameters.
*
* @return upper bound of the support (always
* {@code Double.POSITIVE_INFINITY})
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/** {@inheritDoc} */
public boolean isSupportLowerBoundInclusive() {
return false;
}
/** {@inheritDoc} */
public boolean isSupportUpperBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
/** {@inheritDoc} */
@Override
public double sample() {
return standardDeviation * random.nextGaussian() + mean;
}
}