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    1   /*
    2    * Copyright 2004 The Apache Software Foundation.
    3    *
    4    * Licensed under the Apache License, Version 2.0 (the "License");
    5    * you may not use this file except in compliance with the License.
    6    * You may obtain a copy of the License at
    7    *
    8    *      http://www.apache.org/licenses/LICENSE-2.0
    9    *
    10   * Unless required by applicable law or agreed to in writing, software
    11   * distributed under the License is distributed on an "AS IS" BASIS,
    12   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    13   * See the License for the specific language governing permissions and
    14   * limitations under the License.
    15   */
    16
    17  package org.apache.commons.math.distribution;
    18
    19  import java.io.Serializable;
    20
    21  import org.apache.commons.math.MathException;
    22  import org.apache.commons.math.special.Erf;
    23
    24  /***
    25   * Default implementation of
    26   * {@link org.apache.commons.math.distribution.NormalDistribution}.
    27   *
    28   * @version $Revision: 348519 $ $Date: 2005-11-23 12:12:18 -0700 (Wed, 23 Nov 2005) $
    29   */
    30  public class NormalDistributionImpl extends AbstractContinuousDistribution
    31          implements NormalDistribution, Serializable {
    32
    33      /*** Serializable version identifier */
    34      private static final long serialVersionUID = 8589540077390120676L;
    35
    36      /*** The mean of this distribution. */
    37      private double mean = 0;
    38
    39      /*** The standard deviation of this distribution. */
    40      private double standardDeviation = 1;
    41
    42      /***
    43       * Create a normal distribution using the given mean and standard deviation.
    44       * @param mean mean for this distribution
    45       * @param sd standard deviation for this distribution
    46       */
    47      public NormalDistributionImpl(double mean, double sd){
    48          super();
    49          setMean(mean);
    50          setStandardDeviation(sd);
    51      }
    52
    53      /***
    54       * Creates normal distribution with the mean equal to zero and standard
    55       * deviation equal to one.
    56       */
    57      public NormalDistributionImpl(){
    58          this(0.0, 1.0);
    59      }
    60
    61      /***
    62       * Access the mean.
    63       * @return mean for this distribution
    64       */
    65      public double getMean() {
    66          return mean;
    67      }
    68
    69      /***
    70       * Modify the mean.
    71       * @param mean for this distribution
    72       */
    73      public void setMean(double mean) {
    74          this.mean = mean;
    75      }
    76
    77      /***
    78       * Access the standard deviation.
    79       * @return standard deviation for this distribution
    80       */
    81      public double getStandardDeviation() {
    82          return standardDeviation;
    83      }
    84
    85      /***
    86       * Modify the standard deviation.
    87       * @param sd standard deviation for this distribution
    88       * @throws IllegalArgumentException if <code>sd</code> is not positive.
    89       */
    90      public void setStandardDeviation(double sd) {
    91          if (sd <= 0.0) {
    92              throw new IllegalArgumentException(
    93                  "Standard deviation must be positive.");
    94          }
    95          standardDeviation = sd;
    96      }
    97
    98      /***
    99       * For this disbution, X, this method returns P(X &lt; <code>x</code>).
    100      * @param x the value at which the CDF is evaluated.
    101      * @return CDF evaluted at <code>x</code>.
    102      * @throws MathException if the algorithm fails to converge.
    103      */
    104     public double cumulativeProbability(double x) throws MathException {
    105         return 0.5 * (1.0 + Erf.erf((x - mean) /
    106                 (standardDeviation * Math.sqrt(2.0))));
    107     }
    108
    109     /***
    110      * For this distribution, X, this method returns the critical point x, such
    111      * that P(X &lt; x) = <code>p</code>.
    112      * <p>
    113      * Returns <code>Double.NEGATIVE_INFINITY</code> for p=0 and
    114      * <code>Double.POSITIVE_INFINITY</code> for p=1.
    115      *
    116      * @param p the desired probability
    117      * @return x, such that P(X &lt; x) = <code>p</code>
    118      * @throws MathException if the inverse cumulative probability can not be
    119      *         computed due to convergence or other numerical errors.
    120      * @throws IllegalArgumentException if <code>p</code> is not a valid
    121      *         probability.
    122      */
    123     public double inverseCumulativeProbability(final double p)
    124     throws MathException {
    125         if (p == 0) {
    126             return Double.NEGATIVE_INFINITY;
    127         }
    128         if (p == 1) {
    129             return Double.POSITIVE_INFINITY;
    130         }
    131         return super.inverseCumulativeProbability(p);
    132     }
    133
    134     /***
    135      * Access the domain value lower bound, based on <code>p</code>, used to
    136      * bracket a CDF root.  This method is used by
    137      * {@link #inverseCumulativeProbability(double)} to find critical values.
    138      *
    139      * @param p the desired probability for the critical value
    140      * @return domain value lower bound, i.e.
    141      *         P(X &lt; <i>lower bound</i>) &lt; <code>p</code>
    142      */
    143     protected double getDomainLowerBound(double p) {
    144         double ret;
    145
    146         if (p < .5) {
    147             ret = -Double.MAX_VALUE;
    148         } else {
    149             ret = getMean();
    150         }
    151
    152         return ret;
    153     }
    154
    155     /***
    156      * Access the domain value upper bound, based on <code>p</code>, used to
    157      * bracket a CDF root.  This method is used by
    158      * {@link #inverseCumulativeProbability(double)} to find critical values.
    159      *
    160      * @param p the desired probability for the critical value
    161      * @return domain value upper bound, i.e.
    162      *         P(X &lt; <i>upper bound</i>) &gt; <code>p</code>
    163      */
    164     protected double getDomainUpperBound(double p) {
    165         double ret;
    166
    167         if (p < .5) {
    168             ret = getMean();
    169         } else {
    170             ret = Double.MAX_VALUE;
    171         }
    172
    173         return ret;
    174     }
    175
    176     /***
    177      * Access the initial domain value, based on <code>p</code>, used to
    178      * bracket a CDF root.  This method is used by
    179      * {@link #inverseCumulativeProbability(double)} to find critical values.
    180      *
    181      * @param p the desired probability for the critical value
    182      * @return initial domain value
    183      */
    184     protected double getInitialDomain(double p) {
    185         double ret;
    186
    187         if (p < .5) {
    188             ret = getMean() - getStandardDeviation();
    189         } else if (p > .5) {
    190             ret = getMean() + getStandardDeviation();
    191         } else {
    192             ret = getMean();
    193         }
    194
    195         return ret;
    196     }
    197 }