001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.math4.stat.descriptive.moment;
018
019import java.io.Serializable;
020
021import org.apache.commons.math4.exception.MathIllegalArgumentException;
022import org.apache.commons.math4.exception.NullArgumentException;
023import org.apache.commons.math4.stat.descriptive.AbstractStorelessUnivariateStatistic;
024import org.apache.commons.math4.util.FastMath;
025import org.apache.commons.math4.util.MathArrays;
026import org.apache.commons.math4.util.MathUtils;
027
028/**
029 * Computes the skewness of the available values.
030 * <p>
031 * We use the following (unbiased) formula to define skewness:</p>
032 * <p>
033 * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p>
034 * <p>
035 * where n is the number of values, mean is the {@link Mean} and std is the
036 * {@link StandardDeviation} </p>
037 * <p>
038 * Note that this statistic is undefined for {@code n < 3}.  <code>Double.Nan</code>
039 * is returned when there is not sufficient data to compute the statistic.
040 * Double.NaN may also be returned if the input includes NaN and / or
041 * infinite values.</p>
042 * <p>
043 * <strong>Note that this implementation is not synchronized.</strong> If
044 * multiple threads access an instance of this class concurrently, and at least
045 * one of the threads invokes the <code>increment()</code> or
046 * <code>clear()</code> method, it must be synchronized externally. </p>
047 */
048public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable {
049
050    /** Serializable version identifier */
051    private static final long serialVersionUID = 20150412L;
052
053    /** Third moment on which this statistic is based */
054    protected ThirdMoment moment;
055
056     /**
057     * Determines whether or not this statistic can be incremented or cleared.
058     * <p>
059     * Statistics based on (constructed from) external moments cannot
060     * be incremented or cleared.</p>
061    */
062    protected boolean incMoment;
063
064    /**
065     * Constructs a Skewness.
066     */
067    public Skewness() {
068        incMoment = true;
069        moment = new ThirdMoment();
070    }
071
072    /**
073     * Constructs a Skewness with an external moment.
074     * @param m3 external moment
075     */
076    public Skewness(final ThirdMoment m3) {
077        incMoment = false;
078        this.moment = m3;
079    }
080
081    /**
082     * Copy constructor, creates a new {@code Skewness} identical
083     * to the {@code original}.
084     *
085     * @param original the {@code Skewness} instance to copy
086     * @throws NullArgumentException if original is null
087     */
088    public Skewness(Skewness original) throws NullArgumentException {
089        copy(original, this);
090    }
091
092    /**
093     * {@inheritDoc}
094     * <p>Note that when {@link #Skewness(ThirdMoment)} is used to
095     * create a Skewness, this method does nothing. In that case, the
096     * ThirdMoment should be incremented directly.</p>
097     */
098    @Override
099    public void increment(final double d) {
100        if (incMoment) {
101            moment.increment(d);
102        }
103    }
104
105    /**
106     * Returns the value of the statistic based on the values that have been added.
107     * <p>
108     * See {@link Skewness} for the definition used in the computation.</p>
109     *
110     * @return the skewness of the available values.
111     */
112    @Override
113    public double getResult() {
114
115        if (moment.n < 3) {
116            return Double.NaN;
117        }
118        double variance = moment.m2 / (moment.n - 1);
119        if (variance < 10E-20) {
120            return 0.0d;
121        } else {
122            double n0 = moment.getN();
123            return  (n0 * moment.m3) /
124            ((n0 - 1) * (n0 -2) * FastMath.sqrt(variance) * variance);
125        }
126    }
127
128    /**
129     * {@inheritDoc}
130     */
131    @Override
132    public long getN() {
133        return moment.getN();
134    }
135
136    /**
137     * {@inheritDoc}
138     */
139    @Override
140    public void clear() {
141        if (incMoment) {
142            moment.clear();
143        }
144    }
145
146    /**
147     * Returns the Skewness of the entries in the specified portion of the
148     * input array.
149     * <p>
150     * See {@link Skewness} for the definition used in the computation.</p>
151     * <p>
152     * Throws <code>IllegalArgumentException</code> if the array is null.</p>
153     *
154     * @param values the input array
155     * @param begin the index of the first array element to include
156     * @param length the number of elements to include
157     * @return the skewness of the values or Double.NaN if length is less than 3
158     * @throws MathIllegalArgumentException if the array is null or the array index
159     *  parameters are not valid
160     */
161    @Override
162    public double evaluate(final double[] values,final int begin, final int length)
163        throws MathIllegalArgumentException {
164
165        // Initialize the skewness
166        double skew = Double.NaN;
167
168        if (MathArrays.verifyValues(values, begin, length) && length > 2 ) {
169            Mean mean = new Mean();
170            // Get the mean and the standard deviation
171            double m = mean.evaluate(values, begin, length);
172
173            // Calc the std, this is implemented here instead
174            // of using the standardDeviation method eliminate
175            // a duplicate pass to get the mean
176            double accum = 0.0;
177            double accum2 = 0.0;
178            for (int i = begin; i < begin + length; i++) {
179                final double d = values[i] - m;
180                accum  += d * d;
181                accum2 += d;
182            }
183            final double variance = (accum - (accum2 * accum2 / length)) / (length - 1);
184
185            double accum3 = 0.0;
186            for (int i = begin; i < begin + length; i++) {
187                final double d = values[i] - m;
188                accum3 += d * d * d;
189            }
190            accum3 /= variance * FastMath.sqrt(variance);
191
192            // Get N
193            double n0 = length;
194
195            // Calculate skewness
196            skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3;
197        }
198        return skew;
199    }
200
201    /**
202     * {@inheritDoc}
203     */
204    @Override
205    public Skewness copy() {
206        Skewness result = new Skewness();
207        // No try-catch or advertised exception because args are guaranteed non-null
208        copy(this, result);
209        return result;
210    }
211
212    /**
213     * Copies source to dest.
214     * <p>Neither source nor dest can be null.</p>
215     *
216     * @param source Skewness to copy
217     * @param dest Skewness to copy to
218     * @throws NullArgumentException if either source or dest is null
219     */
220    public static void copy(Skewness source, Skewness dest)
221        throws NullArgumentException {
222        MathUtils.checkNotNull(source);
223        MathUtils.checkNotNull(dest);
224        dest.moment = new ThirdMoment(source.moment.copy());
225        dest.incMoment = source.incMoment;
226    }
227}