/*
* 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.exception.NotStrictlyPositiveException;
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 $Id: NormalDistributionImpl.java 1131229 2011-06-03 20:49:25Z luc $
*/
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);
/** Mean of this distribution. */
private final double mean;
/** Standard deviation of this distribution. */
private final double standardDeviation;
/** 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.
* @throws NotStrictlyPositiveException if {@code sd <= 0}.
* @since 2.1
*/
public NormalDistributionImpl(double mean, double sd, double inverseCumAccuracy) {
if (sd <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.STANDARD_DEVIATION, sd);
}
this.mean = mean;
standardDeviation = sd;
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Create a normal distribution with mean equal to zero and standard
* deviation equal to one.
*/
public NormalDistributionImpl(){
this(0, 1);
}
/**
* {@inheritDoc}
*/
public double getMean() {
return mean;
}
/**
* {@inheritDoc}
*/
public double getStandardDeviation() {
return standardDeviation;
}
/**
* {@inheritDoc}
*/
@Override
public double density(double x) {
final double x0 = x - mean;
final double x1 = x0 / standardDeviation;
return FastMath.exp(-0.5 * x1 * x1) / (standardDeviation * SQRT2PI);
}
/**
* For this distribution, {@code X}, this method returns {@code P(X < x)}.
* 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.
*
* @param x Value at which the CDF is evaluated.
* @return CDF evaluated at {@code x}.
* @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 + Erf.erf(dev / (standardDeviation * FastMath.sqrt(2))));
}
/**
* 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
* {@code x}, such that {@code P(X < x) = p}.
* It will return {@code Double.NEGATIVE_INFINITY} when p = 0 and
* {@code Double.POSITIVE_INFINITY} for p = 1.
*
* @param p Desired probability.
* @return {@code x}, such that {@code P(X < x) = p}.
* @throws MathException if the inverse cumulative probability cannot be
* computed due to convergence or other numerical errors.
* @throws org.apache.commons.math.exception.OutOfRangeException if
* {@code p} 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);
}
/**
* Generate a random value sampled from this distribution.
*
* @return a 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}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the domain value lower bound, i.e. {@code P(X < 'lower bound') < p}.
*/
@Override
protected double getDomainLowerBound(double p) {
double ret;
if (p < 0.5) {
ret = -Double.MAX_VALUE;
} else {
ret = mean;
}
return ret;
}
/**
* Access the domain value upper bound, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the domain value upper bound, i.e. {@code P(X < 'upper bound') > p}.
*/
@Override
protected double getDomainUpperBound(double p) {
double ret;
if (p < 0.5) {
ret = mean;
} else {
ret = Double.MAX_VALUE;
}
return ret;
}
/**
* Access the initial domain value, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the initial domain value.
*/
@Override
protected double getInitialDomain(double p) {
double ret;
if (p < 0.5) {
ret = mean - standardDeviation;
} else if (p > 0.5) {
ret = mean + standardDeviation;
} else {
ret = mean;
}
return ret;
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always negative infinity
* no matter the parameters.
*
* @return lower bound of the support (always Double.NEGATIVE_INFINITY)
*/
@Override
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 Double.POSITIVE_INFINITY)
*/
@Override
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* {@inheritDoc}
*
* For mean parameter <code>mu</code>, the mean is <code>mu</code>
*
* @return {@inheritDoc}
*/
@Override
protected double calculateNumericalMean() {
return getMean();
}
/**
* {@inheritDoc}
*
* For standard deviation parameter <code>s</code>,
* the variance is <code>s^2</code>
*
* @return {@inheritDoc}
*/
@Override
protected double calculateNumericalVariance() {
final double s = getStandardDeviation();
return s * s;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportLowerBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportUpperBoundInclusive() {
return false;
}
}