Skewness.java

  1. /*
  2.  * Licensed to the Apache Software Foundation (ASF) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * The ASF licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *      http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.apache.commons.math4.legacy.stat.descriptive.moment;

  19. import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  20. import org.apache.commons.math4.legacy.exception.NullArgumentException;
  21. import org.apache.commons.math4.legacy.stat.descriptive.AbstractStorelessUnivariateStatistic;
  22. import org.apache.commons.math4.core.jdkmath.JdkMath;
  23. import org.apache.commons.math4.legacy.core.MathArrays;

  25. /**
  26.  * Computes the skewness of the available values.
  27.  * <p>
  28.  * We use the following (unbiased) formula to define skewness:</p>
  29.  * <p>
  30.  * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p>
  31.  * <p>
  32.  * where n is the number of values, mean is the {@link Mean} and std is the
  33.  * {@link StandardDeviation} </p>
  34.  * <p>
  35.  * Note that this statistic is undefined for {@code n < 3}.  <code>Double.Nan</code>
  36.  * is returned when there is not sufficient data to compute the statistic.
  37.  * Double.NaN may also be returned if the input includes NaN and / or
  38.  * infinite values.</p>
  39.  * <p>
  40.  * <strong>Note that this implementation is not synchronized.</strong> If
  41.  * multiple threads access an instance of this class concurrently, and at least
  42.  * one of the threads invokes the <code>increment()</code> or
  43.  * <code>clear()</code> method, it must be synchronized externally. </p>
  44.  */
  45. public class Skewness extends AbstractStorelessUnivariateStatistic {
  46.     /** The value below which the variance is considered zero and thus skewness is zero. */
  47.     private static final double ZERO_VARIANCE_THRESHOLD = 10E-20;

  49.     /** Third moment on which this statistic is based. */
  50.     protected ThirdMoment moment;

  52.      /**
  53.      * Determines whether or not this statistic can be incremented or cleared.
  54.      * <p>
  55.      * Statistics based on (constructed from) external moments cannot
  56.      * be incremented or cleared.</p>
  57.     */
  58.     protected boolean incMoment;

  60.     /**
  61.      * Constructs a Skewness.
  62.      */
  63.     public Skewness() {
  64.         incMoment = true;
  65.         moment = new ThirdMoment();
  66.     }

  68.     /**
  69.      * Constructs a Skewness with an external moment.
  70.      * @param m3 external moment
  71.      */
  72.     public Skewness(final ThirdMoment m3) {
  73.         incMoment = false;
  74.         this.moment = m3;
  75.     }

  77.     /**
  78.      * Copy constructor, creates a new {@code Skewness} identical
  79.      * to the {@code original}.
  80.      *
  81.      * @param original the {@code Skewness} instance to copy
  82.      * @throws NullArgumentException if original is null
  83.      */
  84.     public Skewness(Skewness original) throws NullArgumentException {
  85.         copy(original, this);
  86.     }

  88.     /**
  89.      * {@inheritDoc}
  90.      * <p>Note that when {@link #Skewness(ThirdMoment)} is used to
  91.      * create a Skewness, this method does nothing. In that case, the
  92.      * ThirdMoment should be incremented directly.</p>
  93.      */
  94.     @Override
  95.     public void increment(final double d) {
  96.         if (incMoment) {
  97.             moment.increment(d);
  98.         }
  99.     }

  101.     /**
  102.      * Returns the value of the statistic based on the values that have been added.
  103.      * <p>
  104.      * See {@link Skewness} for the definition used in the computation.</p>
  105.      *
  106.      * @return the skewness of the available values.
  107.      */
  108.     @Override
  109.     public double getResult() {

  111.         if (moment.n < 3) {
  112.             return Double.NaN;
  113.         }
  114.         double variance = moment.m2 / (moment.n - 1);
  115.         if (variance < ZERO_VARIANCE_THRESHOLD) {
  116.             return 0.0d;
  117.         } else {
  118.             double n0 = moment.getN();
  119.             return  (n0 * moment.m3) /
  120.             ((n0 - 1) * (n0 -2) * JdkMath.sqrt(variance) * variance);
  121.         }
  122.     }

  124.     /**
  125.      * {@inheritDoc}
  126.      */
  127.     @Override
  128.     public long getN() {
  129.         return moment.getN();
  130.     }

  132.     /**
  133.      * {@inheritDoc}
  134.      */
  135.     @Override
  136.     public void clear() {
  137.         if (incMoment) {
  138.             moment.clear();
  139.         }
  140.     }

  142.     /**
  143.      * Returns the Skewness of the entries in the specified portion of the
  144.      * input array.
  145.      * <p>
  146.      * See {@link Skewness} for the definition used in the computation.</p>
  147.      * <p>
  148.      * Throws <code>IllegalArgumentException</code> if the array is null.</p>
  149.      *
  150.      * @param values the input array
  151.      * @param begin the index of the first array element to include
  152.      * @param length the number of elements to include
  153.      * @return the skewness of the values or Double.NaN if length is less than 3
  154.      * @throws MathIllegalArgumentException if the array is null or the array index
  155.      *  parameters are not valid
  156.      */
  157.     @Override
  158.     public double evaluate(final double[] values,final int begin, final int length)
  159.         throws MathIllegalArgumentException {

  161.         // Initialize the skewness
  162.         double skew = Double.NaN;

  164.         if (MathArrays.verifyValues(values, begin, length) && length > 2 ) {
  165.             Mean mean = new Mean();
  166.             // Get the mean and the standard deviation
  167.             double m = mean.evaluate(values, begin, length);

  169.             // Calc the std, this is implemented here instead
  170.             // of using the standardDeviation method eliminate
  171.             // a duplicate pass to get the mean
  172.             double accum = 0.0;
  173.             double accum2 = 0.0;
  174.             for (int i = begin; i < begin + length; i++) {
  175.                 final double d = values[i] - m;
  176.                 accum  += d * d;
  177.                 accum2 += d;
  178.             }
  179.             final double variance = (accum - (accum2 * accum2 / length)) / (length - 1);
  180.             if (variance < ZERO_VARIANCE_THRESHOLD) {
  181.                 skew = 0.0d;
  182.             } else {
  183.                 double accum3 = 0.0;
  184.                 for (int i = begin; i < begin + length; i++) {
  185.                     final double d = values[i] - m;
  186.                     accum3 += d * d * d;
  187.                 }
  188.                 accum3 /= variance * JdkMath.sqrt(variance);

  190.                 // Get N
  191.                 double n0 = length;

  193.                 // Calculate skewness
  194.                 skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3;
  195.             }
  196.         }
  197.         return skew;
  198.     }

  200.     /**
  201.      * {@inheritDoc}
  202.      */
  203.     @Override
  204.     public Skewness copy() {
  205.         Skewness result = new Skewness();
  206.         // No try-catch or advertised exception because args are guaranteed non-null
  207.         copy(this, result);
  208.         return result;
  209.     }

  211.     /**
  212.      * Copies source to dest.
  213.      * <p>Neither source nor dest can be null.</p>
  214.      *
  215.      * @param source Skewness to copy
  216.      * @param dest Skewness to copy to
  217.      * @throws NullArgumentException if either source or dest is null
  218.      */
  219.     public static void copy(Skewness source, Skewness dest)
  220.         throws NullArgumentException {
  221.         NullArgumentException.check(source);
  222.         NullArgumentException.check(dest);
  223.         dest.moment = new ThirdMoment(source.moment.copy());
  224.         dest.incMoment = source.incMoment;
  225.     }
  226. }
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