Commons Math example source code file (NormalDistributionImpl.java)

This example Commons Math source code file (NormalDistributionImpl.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" ^TM.

Java - Commons Math tags/keywords

default_inverse_absolute_accuracy, default_inverse_absolute_accuracy, deprecated, io, jdk, mathexception, maxiterationsexceededexception, normaldistribution, normaldistributionimpl, normaldistributionimpl, override, override, serializable, sqrt2pi, sqrt2pi

The Commons Math NormalDistributionImpl.java source code

/*
 * 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.MaxIterationsExceededException;
import org.apache.commons.math.special.Erf;

/**
 * Default implementation of
 * {@link org.apache.commons.math.distribution.NormalDistribution}.
 *
 * @version $Revision: 925812 $ $Date: 2010-03-21 11:49:31 -0400 (Sun, 21 Mar 2010) $
 */
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 = Math.sqrt(2 * Math.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 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 is not positive.
     */
    private void setStandardDeviationInternal(double sd) {
        if (sd <= 0.0) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "standard deviation must be positive ({0})",
                  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
     */
    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
     */
    public double density(double x) {
        double x0 = x - mean;
        return Math.exp(-x0 * x0 / (2 * standardDeviation * standardDeviation)) / (standardDeviation * SQRT2PI);
    }

    /**
     * For this distribution, X, this method returns P(X < <code>x).
     * @param x the value at which the CDF is evaluated.
     * @return CDF evaluted at <code>x.
     * @throws MathException if the algorithm fails to converge; unless
     * x is more than 20 standard deviations from the mean, in which case the
     * convergence exception is caught and 0 or 1 is returned.
     */
    public double cumulativeProbability(double x) throws MathException {
        try {
            return 0.5 * (1.0 + Erf.erf((x - mean) /
                    (standardDeviation * Math.sqrt(2.0))));
        } catch (MaxIterationsExceededException ex) {
            if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
                return 0.0d;
            } else if (x > (mean + 20 * standardDeviation)) {
                return 1.0d;
            } else {
                throw ex;
            }
        }
    }

    /**
     * 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.
     * <p>
     * Returns <code>Double.NEGATIVE_INFINITY for p=0 and
     * <code>Double.POSITIVE_INFINITY for p=1.

     *
     * @param p the desired probability
     * @return x, such that P(X < x) = <code>p
     * @throws MathException if the inverse cumulative probability can not be
     *         computed due to convergence or other numerical errors.
     * @throws IllegalArgumentException 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);
    }

    /**
     * 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 the desired probability for the critical value
     * @return domain value lower bound, i.e.
     *         P(X < <i>lower bound) < p
     */
    @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, 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) > p
     */
    @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, 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;
    }
}