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1 | /* | |
2 | * Copyright (c) 2003, the JUNG Project and the Regents of the University | |
3 | * of California | |
4 | * All rights reserved. | |
5 | * | |
6 | * This software is open-source under the BSD license; see either | |
7 | * "license.txt" or | |
8 | * http://jung.sourceforge.net/license.txt for a description. | |
9 | */ | |
10 | package edu.uci.ics.jung.statistics; | |
11 | ||
12 | /** | |
13 | * A data structure representing the central moments of a distribution including: <ul> | |
14 | * <li> the mean </li> | |
15 | * <li> the variance </li> | |
16 | * <li> the skewness</li> | |
17 | * <li> the kurtosis </li></ul> <br> | |
18 | * Data values that are observed are passed into this data structure via the accumulate(...) method | |
19 | * and the corresponding central moments are updated on each call | |
20 | * | |
21 | * @author Didier H. Besset (modified by Scott White) | |
22 | */ | |
23 | public class StatisticalMoments { | |
24 | /** | |
25 | * Vector containing the points. | |
26 | */ | |
27 | protected double[] moments; | |
28 | ||
29 | /** | |
30 | * Default constructor methods: declare space for 5 moments. | |
31 | */ | |
32 | public StatisticalMoments() { | |
33 | 4 | this(5); |
34 | 4 | } |
35 | ||
36 | /** | |
37 | * General constructor methods. | |
38 | * @param n number of moments to accumulate. | |
39 | */ | |
40 | 4 | public StatisticalMoments(int n) { |
41 | 4 | moments = new double[n]; |
42 | 4 | reset(); |
43 | 4 | } |
44 | ||
45 | /** | |
46 | * statistical moment accumulation up to order 4. | |
47 | * @param x double value to accumulate | |
48 | */ | |
49 | public void accumulate(double x) { | |
50 | 1010 | double n = moments[0]; |
51 | 1010 | double n1 = n + 1; |
52 | 1010 | double n2 = n * n; |
53 | 1010 | double delta = (moments[1] - x) / n1; |
54 | 1010 | double d2 = delta * delta; |
55 | 1010 | double d3 = delta * d2; |
56 | 1010 | double r1 = (double) n / (double) n1; |
57 | 1010 | moments[4] += 4 * delta * moments[3] + 6 * d2 * moments[2] |
58 | + (1 + n * n2) * d2 * d2; | |
59 | 1010 | moments[4] *= r1; |
60 | 1010 | moments[3] += 3 * delta * moments[2] + (1 - n2) * d3; |
61 | 1010 | moments[3] *= r1; |
62 | 1010 | moments[2] += (1 + n) * d2; |
63 | 1010 | moments[2] *= r1; |
64 | 1010 | moments[1] -= delta; |
65 | 1010 | moments[0] = n1; |
66 | 1010 | return; |
67 | } | |
68 | ||
69 | /** | |
70 | * @return double average. | |
71 | */ | |
72 | public double average() { | |
73 | 2 | return moments[1]; |
74 | } | |
75 | ||
76 | /** | |
77 | * Returns the number of accumulated counts. | |
78 | * @return number of counts. | |
79 | */ | |
80 | public long count() { | |
81 | 0 | return (long) moments[0]; |
82 | } | |
83 | ||
84 | /** | |
85 | * Returns the error on average. May throw divide by zero exception. | |
86 | * @return error on average. | |
87 | */ | |
88 | public double errorOnAverage() { | |
89 | 0 | return Math.sqrt(variance() / moments[0]); |
90 | } | |
91 | ||
92 | /** | |
93 | * The kurtosis measures the sharpness of the distribution near | |
94 | * the maximum. | |
95 | * Note: The kurtosis of the Normal distribution is 0 by definition. | |
96 | * @return double kurtosis or NaN. | |
97 | */ | |
98 | public double kurtosis() throws ArithmeticException { | |
99 | 0 | if (moments[0] < 4) |
100 | 0 | return Double.NaN; |
101 | 0 | double kFact = (moments[0] - 2) * (moments[0] - 3); |
102 | 0 | double n1 = moments[0] - 1; |
103 | 0 | double v = variance(); |
104 | 0 | return (moments[4] * moments[0] * moments[0] * (moments[0] + 1) |
105 | / (v * v * n1) - n1 * n1 * 3) / kFact; | |
106 | } | |
107 | ||
108 | /** | |
109 | * Reset all counters. | |
110 | */ | |
111 | public void reset() { | |
112 | 24 | for (int n = 0; n < moments.length; n++) |
113 | 20 | moments[n] = 0; |
114 | 4 | } |
115 | ||
116 | /** | |
117 | * @return double skewness. | |
118 | */ | |
119 | public double skewness() throws ArithmeticException { | |
120 | 0 | if (moments[0] < 3) |
121 | 0 | return Double.NaN; |
122 | 0 | double v = variance(); |
123 | 0 | return moments[3] * moments[0] * moments[0] |
124 | / (Math.sqrt(v) * v * (moments[0] - 1) | |
125 | * (moments[0] - 2)); | |
126 | } | |
127 | ||
128 | /** | |
129 | * Returns the standard deviation. May throw divide by zero exception. | |
130 | * @return double standard deviation. | |
131 | */ | |
132 | public double standardDeviation() { | |
133 | 0 | return Math.sqrt(variance()); |
134 | } | |
135 | ||
136 | /** | |
137 | * @return double | |
138 | */ | |
139 | public double unnormalizedVariance() { | |
140 | 0 | return moments[2] * moments[0]; |
141 | } | |
142 | ||
143 | /** | |
144 | * Note: the variance includes the Bessel correction factor. | |
145 | * @return double variance. | |
146 | */ | |
147 | public double variance() throws ArithmeticException { | |
148 | 0 | if (moments[0] < 2) |
149 | 0 | return Double.NaN; |
150 | 0 | return unnormalizedVariance() / (moments[0] - 1); |
151 | } | |
152 | } |
this report was generated by version 1.0.5 of jcoverage. |
copyright © 2003, jcoverage ltd. all rights reserved. |