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.math.stat.descriptive.moment; 18 19 import java.io.Serializable; 20 21 /** 22 * Computes a statistic related to the Fourth Central Moment. Specifically, 23 * what is computed is the sum of 24 * <p> 25 * (x_i - xbar) ^ 4, </p> 26 * <p> 27 * where the x_i are the 28 * sample observations and xbar is the sample mean. </p> 29 * <p> 30 * The following recursive updating formula is used: </p> 31 * <p> 32 * Let <ul> 33 * <li> dev = (current obs - previous mean) </li> 34 * <li> m2 = previous value of {@link SecondMoment} </li> 35 * <li> m2 = previous value of {@link ThirdMoment} </li> 36 * <li> n = number of observations (including current obs) </li> 37 * </ul> 38 * Then </p> 39 * <p> 40 * new value = old value - 4 * (dev/n) * m3 + 6 * (dev/n)^2 * m2 + <br> 41 * [n^2 - 3 * (n-1)] * dev^4 * (n-1) / n^3 </p> 42 * <p> 43 * Returns <code>Double.NaN</code> if no data values have been added and 44 * returns <code>0</code> if there is just one value in the data set. </p> 45 * <p> 46 * <strong>Note that this implementation is not synchronized.</strong> If 47 * multiple threads access an instance of this class concurrently, and at least 48 * one of the threads invokes the <code>increment()</code> or 49 * <code>clear()</code> method, it must be synchronized externally. </p> 50 * 51 * @version $Revision: 617953 $ $Date: 2008-02-02 22:54:00 -0700 (Sat, 02 Feb 2008) $ 52 */ 53 public class FourthMoment extends ThirdMoment implements Serializable{ 54 55 /** Serializable version identifier */ 56 private static final long serialVersionUID = 4763990447117157611L; 57 58 /** fourth moment of values that have been added */ 59 protected double m4; 60 61 /** 62 * Create a FourthMoment instance 63 */ 64 public FourthMoment() { 65 super(); 66 m4 = Double.NaN; 67 } 68 69 /** 70 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#increment(double) 71 */ 72 public void increment(final double d) { 73 if (n < 1) { 74 m4 = 0.0; 75 m3 = 0.0; 76 m2 = 0.0; 77 m1 = 0.0; 78 } 79 80 double prevM3 = m3; 81 double prevM2 = m2; 82 83 super.increment(d); 84 85 double n0 = (double) n; 86 87 m4 = m4 - 4.0 * nDev * prevM3 + 6.0 * nDevSq * prevM2 + 88 ((n0 * n0) - 3 * (n0 -1)) * (nDevSq * nDevSq * (n0 - 1) * n0); 89 } 90 91 /** 92 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getResult() 93 */ 94 public double getResult() { 95 return m4; 96 } 97 98 /** 99 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#clear() 100 */ 101 public void clear() { 102 super.clear(); 103 m4 = Double.NaN; 104 } 105 106 }