Classes in this File | Line Coverage | Branch Coverage | Complexity | ||||||||
Kurtosis |
|
| 2.142857142857143;2.143 |
1 | /* |
|
2 | * Copyright 2003-2004 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 | package org.apache.commons.math.stat.descriptive.moment; |
|
17 | ||
18 | import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic; |
|
19 | ||
20 | /** |
|
21 | * Computes the Kurtosis of the available values. |
|
22 | * <p> |
|
23 | * We use the following (unbiased) formula to define kurtosis: |
|
24 | * <p> |
|
25 | * kurtosis = { [n(n+1) / (n -1)(n - 2)(n-3)] sum[(x_i - mean)^4] / std^4 } - [3(n-1)^2 / (n-2)(n-3)] |
|
26 | * <p> |
|
27 | * where n is the number of values, mean is the {@link Mean} and std is the |
|
28 | * {@link StandardDeviation} |
|
29 | * <p> |
|
30 | * Note that this statistic is undefined for n < 4. <code>Double.Nan</code> |
|
31 | * is returned when there is not sufficient data to compute the statistic. |
|
32 | * <p> |
|
33 | * <strong>Note that this implementation is not synchronized.</strong> If |
|
34 | * multiple threads access an instance of this class concurrently, and at least |
|
35 | * one of the threads invokes the <code>increment()</code> or |
|
36 | * <code>clear()</code> method, it must be synchronized externally. |
|
37 | * |
|
38 | * @version $Revision$ $Date: 2005-02-26 05:11:52 -0800 (Sat, 26 Feb 2005) $ |
|
39 | */ |
|
40 | public class Kurtosis extends AbstractStorelessUnivariateStatistic { |
|
41 | ||
42 | /** Serializable version identifier */ |
|
43 | static final long serialVersionUID = 2784465764798260919L; |
|
44 | ||
45 | /**Fourth Moment on which this statistic is based */ |
|
46 | protected FourthMoment moment; |
|
47 | ||
48 | /** |
|
49 | * Determines whether or not this statistic can be incremented or cleared. |
|
50 | * <p> |
|
51 | * Statistics based on (constructed from) external moments cannot |
|
52 | * be incremented or cleared. |
|
53 | */ |
|
54 | protected boolean incMoment; |
|
55 | ||
56 | /** |
|
57 | * Construct a Kurtosis |
|
58 | */ |
|
59 | 32 | public Kurtosis() { |
60 | 32 | incMoment = true; |
61 | 32 | moment = new FourthMoment(); |
62 | 32 | } |
63 | ||
64 | /** |
|
65 | * Construct a Kurtosis from an external moment |
|
66 | * |
|
67 | * @param m4 external Moment |
|
68 | */ |
|
69 | 2 | public Kurtosis(final FourthMoment m4) { |
70 | 2 | incMoment = false; |
71 | 2 | this.moment = m4; |
72 | 2 | } |
73 | ||
74 | /** |
|
75 | * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#increment(double) |
|
76 | */ |
|
77 | public void increment(final double d) { |
|
78 | 168 | if (incMoment) { |
79 | 168 | moment.increment(d); |
80 | } else { |
|
81 | 0 | throw new IllegalStateException |
82 | ("Statistics constructed from external moments cannot be incremented"); |
|
83 | } |
|
84 | 168 | } |
85 | ||
86 | /** |
|
87 | * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getResult() |
|
88 | */ |
|
89 | public double getResult() { |
|
90 | 98 | double kurtosis = Double.NaN; |
91 | 98 | if (moment.getN() > 3) { |
92 | 20 | double variance = moment.m2 / (double) (moment.n - 1); |
93 | 20 | if (moment.n <= 3 || variance < 10E-20) { |
94 | 2 | kurtosis = 0.0; |
95 | } else { |
|
96 | 18 | double n = (double) moment.n; |
97 | 18 | kurtosis = |
98 | (n * (n + 1) * moment.m4 - |
|
99 | 3 * moment.m2 * moment.m2 * (n - 1)) / |
|
100 | ((n - 1) * (n -2) * (n -3) * variance * variance); |
|
101 | } |
|
102 | } |
|
103 | 98 | return kurtosis; |
104 | } |
|
105 | ||
106 | /** |
|
107 | * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#clear() |
|
108 | */ |
|
109 | public void clear() { |
|
110 | 22 | if (incMoment) { |
111 | 22 | moment.clear(); |
112 | } else { |
|
113 | 0 | throw new IllegalStateException |
114 | ("Statistics constructed from external moments cannot be cleared"); |
|
115 | } |
|
116 | 22 | } |
117 | ||
118 | /** |
|
119 | * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getN() |
|
120 | */ |
|
121 | public long getN() { |
|
122 | 70 | return moment.getN(); |
123 | } |
|
124 | ||
125 | /* UnvariateStatistic Approach */ |
|
126 | ||
127 | /** |
|
128 | * Returns the kurtosis of the entries in the specified portion of the |
|
129 | * input array. |
|
130 | * <p> |
|
131 | * See {@link Kurtosis} for details on the computing algorithm. |
|
132 | * <p> |
|
133 | * Throws <code>IllegalArgumentException</code> if the array is null. |
|
134 | * |
|
135 | * @param values the input array |
|
136 | * @param begin index of the first array element to include |
|
137 | * @param length the number of elements to include |
|
138 | * @return the kurtosis of the values or Double.NaN if length is less than |
|
139 | * 4 |
|
140 | * @throws IllegalArgumentException if the input array is null or the array |
|
141 | * index parameters are not valid |
|
142 | */ |
|
143 | public double evaluate(final double[] values,final int begin, final int length) { |
|
144 | // Initialize the kurtosis |
|
145 | 30 | double kurt = Double.NaN; |
146 | ||
147 | 30 | if (test(values, begin, length) && length > 3) { |
148 | ||
149 | // Compute the mean and standard deviation |
|
150 | 18 | Variance variance = new Variance(); |
151 | 18 | variance.incrementAll(values, begin, length); |
152 | 18 | double mean = variance.moment.m1; |
153 | 18 | double stdDev = Math.sqrt(variance.getResult()); |
154 | ||
155 | // Sum the ^4 of the distance from the mean divided by the |
|
156 | // standard deviation |
|
157 | 18 | double accum3 = 0.0; |
158 | 378 | for (int i = begin; i < begin + length; i++) { |
159 | 360 | accum3 += Math.pow((values[i] - mean), 4.0); |
160 | } |
|
161 | 18 | accum3 /= Math.pow(stdDev, 4.0d); |
162 | ||
163 | // Get N |
|
164 | 18 | double n0 = length; |
165 | ||
166 | 18 | double coefficientOne = |
167 | (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3)); |
|
168 | 18 | double termTwo = |
169 | ((3 * Math.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3))); |
|
170 | ||
171 | // Calculate kurtosis |
|
172 | 18 | kurt = (coefficientOne * accum3) - termTwo; |
173 | } |
|
174 | 30 | return kurt; |
175 | } |
|
176 | ||
177 | } |