Source Code Cross Referenced for Skewness.java in  » Science » Apache-commons-math-1.1 » org » apache » commons » math » stat » descriptive » moment » Java Source Code / Java DocumentationJava Source Code and Java Documentation

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Java Source Code / Java Documentation » Science » Apache commons math 1.1 » org.apache.commons.math.stat.descriptive.moment 
Source Cross Referenced  Class Diagram Java Document (Java Doc) 


001:        /*
002:         * Copyright 2003-2004 The Apache Software Foundation.
003:         *
004:         * Licensed under the Apache License, Version 2.0 (the "License");
005:         * you may not use this file except in compliance with the License.
006:         * You may obtain a copy of the License at
007:         *
008:         *      http://www.apache.org/licenses/LICENSE-2.0
009:         *
010:         * Unless required by applicable law or agreed to in writing, software
011:         * distributed under the License is distributed on an "AS IS" BASIS,
012:         * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
013:         * See the License for the specific language governing permissions and
014:         * limitations under the License.
015:         */
016:        package org.apache.commons.math.stat.descriptive.moment;
017:
018:        import java.io.Serializable;
019:
020:        import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
021:
022:        /**
023:         * Computes the skewness of the available values.
024:         * <p>
025:         * We use the following (unbiased) formula to define skewness:
026:         * <p>
027:         * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3
028:         * <p>
029:         * where n is the number of values, mean is the {@link Mean} and std is the 
030:         * {@link StandardDeviation}
031:         * <p>
032:         * <strong>Note that this implementation is not synchronized.</strong> If 
033:         * multiple threads access an instance of this class concurrently, and at least
034:         * one of the threads invokes the <code>increment()</code> or 
035:         * <code>clear()</code> method, it must be synchronized externally.
036:         * 
037:         * @version $Revision: 348519 $ $Date: 2005-11-23 12:12:18 -0700 (Wed, 23 Nov 2005) $
038:         */
039:        public class Skewness extends AbstractStorelessUnivariateStatistic
040:                implements  Serializable {
041:
042:            /** Serializable version identifier */
043:            private static final long serialVersionUID = 7101857578996691352L;
044:
045:            /** Third moment on which this statistic is based */
046:            protected ThirdMoment moment = null;
047:
048:            /** 
049:             * Determines whether or not this statistic can be incremented or cleared.
050:             * <p>
051:             * Statistics based on (constructed from) external moments cannot
052:             * be incremented or cleared.
053:             */
054:            protected boolean incMoment;
055:
056:            /**
057:             * Constructs a Skewness
058:             */
059:            public Skewness() {
060:                incMoment = true;
061:                moment = new ThirdMoment();
062:            }
063:
064:            /**
065:             * Constructs a Skewness with an external moment
066:             * @param m3 external moment
067:             */
068:            public Skewness(final ThirdMoment m3) {
069:                incMoment = false;
070:                this .moment = m3;
071:            }
072:
073:            /**
074:             * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#increment(double)
075:             */
076:            public void increment(final double d) {
077:                if (incMoment) {
078:                    moment.increment(d);
079:                }
080:            }
081:
082:            /**
083:             * Returns the value of the statistic based on the values that have been added.
084:             * <p>
085:             * See {@link Skewness} for the definition used in the computation.
086:             * 
087:             * @return the skewness of the available values.
088:             */
089:            public double getResult() {
090:
091:                if (moment.n < 3) {
092:                    return Double.NaN;
093:                }
094:                double variance = moment.m2 / (double) (moment.n - 1);
095:                if (variance < 10E-20) {
096:                    return 0.0d;
097:                } else {
098:                    double n0 = (double) moment.getN();
099:                    return (n0 * moment.m3)
100:                            / ((n0 - 1) * (n0 - 2) * Math.sqrt(variance) * variance);
101:                }
102:            }
103:
104:            /**
105:             * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getN()
106:             */
107:            public long getN() {
108:                return moment.getN();
109:            }
110:
111:            /**
112:             * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#clear()
113:             */
114:            public void clear() {
115:                if (incMoment) {
116:                    moment.clear();
117:                }
118:            }
119:
120:            /**
121:             * Returns the Skewness of the entries in the specifed portion of the
122:             * input array.
123:             * <p>
124:             * See {@link Skewness} for the definition used in the computation.
125:             * <p>
126:             * Throws <code>IllegalArgumentException</code> if the array is null.
127:             * 
128:             * @param values the input array
129:             * @param begin the index of the first array element to include
130:             * @param length the number of elements to include
131:             * @return the skewness of the values or Double.NaN if length is less than
132:             * 3
133:             * @throws IllegalArgumentException if the array is null or the array index
134:             *  parameters are not valid
135:             */
136:            public double evaluate(final double[] values, final int begin,
137:                    final int length) {
138:
139:                // Initialize the skewness
140:                double skew = Double.NaN;
141:
142:                if (test(values, begin, length) && length > 2) {
143:                    Mean mean = new Mean();
144:                    // Get the mean and the standard deviation
145:                    double m = mean.evaluate(values, begin, length);
146:
147:                    // Calc the std, this is implemented here instead
148:                    // of using the standardDeviation method eliminate
149:                    // a duplicate pass to get the mean
150:                    double accum = 0.0;
151:                    double accum2 = 0.0;
152:                    for (int i = begin; i < begin + length; i++) {
153:                        accum += Math.pow((values[i] - m), 2.0);
154:                        accum2 += (values[i] - m);
155:                    }
156:                    double stdDev = Math
157:                            .sqrt((accum - (Math.pow(accum2, 2) / ((double) length)))
158:                                    / (double) (length - 1));
159:
160:                    double accum3 = 0.0;
161:                    for (int i = begin; i < begin + length; i++) {
162:                        accum3 += Math.pow(values[i] - m, 3.0d);
163:                    }
164:                    accum3 /= Math.pow(stdDev, 3.0d);
165:
166:                    // Get N
167:                    double n0 = length;
168:
169:                    // Calculate skewness
170:                    skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3;
171:                }
172:                return skew;
173:            }
174:        }
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