| /* |
| * 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.random.RandomGenerator; |
| import org.apache.commons.math3.random.Well19937c; |
| import org.apache.commons.math3.special.Erf; |
| import org.apache.commons.math3.util.FastMath; |
| |
| /** |
| * 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. |
| * <p> |
| * <b>Note:</b> this constructor will implicitly create an instance of |
| * {@link Well19937c} as random generator to be used for sampling only (see |
| * {@link #sample()} and {@link #sample(int)}). In case no sampling is |
| * needed for the created distribution, it is advised to pass {@code null} |
| * as random generator via the appropriate constructors to avoid the |
| * additional initialisation overhead. |
| */ |
| public NormalDistribution() { |
| this(0, 1); |
| } |
| |
| /** |
| * Create a normal distribution using the given mean and standard deviation. |
| * <p> |
| * <b>Note:</b> this constructor will implicitly create an instance of |
| * {@link Well19937c} as random generator to be used for sampling only (see |
| * {@link #sample()} and {@link #sample(int)}). In case no sampling is |
| * needed for the created distribution, it is advised to pass {@code null} |
| * as random generator via the appropriate constructors to avoid the |
| * additional initialisation overhead. |
| * |
| * @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. |
| * <p> |
| * <b>Note:</b> this constructor will implicitly create an instance of |
| * {@link Well19937c} as random generator to be used for sampling only (see |
| * {@link #sample()} and {@link #sample(int)}). In case no sampling is |
| * needed for the created distribution, it is advised to pass {@code null} |
| * as random generator via the appropriate constructors to avoid the |
| * additional initialisation overhead. |
| * |
| * @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 * Erf.erfc(-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; |
| } |
| } |
