Java tutorial
/* * 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.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> * @version $Id: NormalDistribution.java 1416643 2012-12-03 19:37:14Z tn $ */ 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 π) */ private static final double SQRT2PI = FastMath.sqrt(2 * FastMath.PI); /** √(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; /** 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. * @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; 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) { final double x0 = x - mean; final double x1 = x0 / standardDeviation; return FastMath.exp(-0.5 * x1 * x1) / (standardDeviation * SQRT2PI); } /** * {@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} * * @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; } }