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1 NAME
2 StatisticsUtil
3
4 SYNOPSIS
5 use StatisticsUtil;
6
7 use Statistics qw(:all);
8
9 DESCRIPTION
10 StatisticsUtil module provides the following functions:
11
12 Average, AverageDeviation, Correlation, Covariance, Euclidean,
13 Factorial, FactorialDivison, Frequency, GeometricMean, HarmonicMean,
14 KLargest, KSmallest, Kurtosis, Maximum, Mean, Median, Minimum, Mode,
15 PearsonCorrelation, Permutations, Product, RSquare, Range, Skewness,
16 StandardDeviation, StandardDeviationN, StandardError, StandardScores,
17 StandardScoresN, Standardize, Sum, SumOfSquares, TrimMean, Variance,
18 VarianceN
19
20 METHODS
21 Average
22 $Value = Average(\@DataArray);
23
24 Computes the mean of an array of numbers: SUM( x[i] ) / n
25
26 AverageDeviation
27 $Value = AverageDeviation(\@DataArray);
28
29 Computes the average of the absolute deviation of an array of
30 numbers: SUM( ABS(x[i] - Xmean) ) / n
31
32 Correlation
33 $Value = Correlation(\@XDataArray, \@YDataArray);
34
35 Computes the Pearson correlation coefficient between two arrays of
36 numbers: SUM( (x[i] - Xmean)(y[i] - Ymean) ) / SQRT( SUM( (x[i] -
37 Xmean)^2 )(SUM( (y[i] - Ymean)^2 )) )
38
39 Euclidean
40 $Return = Euclidean(\@DataArray);
41
42 Computes the euclidean distance of an array of numbers: SQRT( SUM(
43 x[i] ** 2) )
44
45 Covariance
46 $Value = Covariance(\@XDataArray, \@YDataArray);
47
48 Computes the covariance between two arrays of numbers: SUM( (x[i] -
49 Xmean) (y[i] - Ymean) ) / n
50
51 Factorial
52 $Value = Factorial($Num);
53
54 Computes the factorial of a positive integer.
55
56 FactorialDivison
57 $Value = FactorialDivision($Numerator, $Denominator);
58
59 Compute the factorial divison of two positive integers.
60
61 Frequency
62 %FrequencyValues = Frequency(\@DataArray, [$NumOfBins]);
63 %FrequencyValues = Frequency(\@DataArray, [\@BinRange]);
64
65 A hash array is returned with keys and values representing range and
66 frequency values, respectively. The frequency value for a specific
67 key corresponds to all the values which are greater than the
68 previous key and less than or equal to the current key. A key value
69 representing maximum value is added for generating frequency
70 distribution for specific number of bins, and whenever the maximum
71 array value is greater than the maximum specified in bin range, it
72 is also added to bin range.
73
74 GeometricMean
75 $Value = GeometricMean(\@DataArray);
76
77 Computes the geometric mean of an array of numbers: NthROOT(
78 PRODUCT(x[i]) )
79
80 HarmonicMean
81 $Value = HarmonicMean(\@DataArray);
82
83 Computes the harmonic mean of an array of numbers: 1 / ( SUM(1/x[i])
84 / n )
85
86 KLargest
87 $Value = KLargest(\@DataArray, $KthNumber);
88
89 Returns the k-largest value from an array of numbers.
90
91 KSmallest
92 $Value = KSmallest(\@DataArray, $KthNumber);
93
94 Returns the k-smallest value from an array of numbers.
95
96 Kurtosis
97 $Value = Kurtosis(\@DataArray);
98
99 Computes the kurtosis of an array of numbers: [ {n(n + 1)/(n - 1)(n
100 - 2)(n - 3)} SUM{ ((x[i] - Xmean)/STDDEV)^4 } ] - {3((n - 1)^2)}/{(n
101 - 2)(n-3)}
102
103 Maximum
104 $Value = Maximum(\@DataArray);
105
106 Returns the largest value from an array of numbers.
107
108 Minimum
109 $Value = Minimum(\@DataArray);
110
111 Returns the smallest value from an array of numbers.
112
113 Mean
114 $Value = Mean(\@DataArray);
115
116 Computes the mean of an array of numbers: SUM( x[i] ) / n
117
118 Median
119 $Value = Median(\@DataArray);
120
121 Computes the median value of an array of numbers. For an even number
122 array, it's the average of two middle values.
123
124 For even values of n: Xsorted[(n - 1)/2 + 1] For odd values of n:
125 (Xsorted[n/2] + Xsorted[n/2 + 1])/2
126
127 Mode
128 $Value = Mode(\@DataArray);
129
130 Returns the most frequently occuring value in an array of numbers.
131
132 PearsonCorrelation
133 $Value = Correlation(\@XDataArray, \@YDataArray);
134
135 Computes the Pearson correlation coefficient between two arrays of
136 numbers: SUM( (x[i] - Xmean)(y[i] - Ymean) ) / SQRT( SUM( (x[i] -
137 Xmean)^2 )(SUM( (y[i] - Ymean)^2 )) )
138
139 Permutations
140 $PermutationsRef = Permutations(@DataToPermute);
141
142 Generate all possible permuations or a specific permutations of
143 items in an array and return a reference to an array containing
144 array references to generated permuations.
145
146 This alogrithm is based on the example provided by Mark
147 Jason-Dominus, and is available at CPAN as mjd_permute standalone
148 script.
149
150 Product
151 $Value = Product(\@DataArray);
152
153 Compute the product of an array of numbers.
154
155 Range
156 ($Smallest, $Largest) = Range(\@DataArray);
157
158 Return the smallest and largest values from an array of numbers.
159
160 RSquare
161 $Value = RSquare(\@XDataArray, \@YDataArray);
162
163 Computes square of the Pearson correlation coefficient between two
164 arrays of numbers.
165
166 Skewness
167 $Value = Skewness(\@DataArray);
168
169 Computes the skewness of an array of numbers: {n/(n - 1)(n - 2)}
170 SUM{ ((x[i] - Xmean)/STDDEV)^3 }
171
172 StandardDeviation
173 $Value = StandardDeviation(\@DataArray);
174
175 Computes the standard deviation of an array of numbers. SQRT ( SUM(
176 (x[i] - mean)^2 ) / (n - 1) )
177
178 StandardDeviationN
179 $Value = StandardDeviationN(\@DataArray);
180
181 Computes the standard deviation of an array of numbers representing
182 entire population: SQRT ( SUM( (x[i] - mean)^2 ) / n )
183
184 StandardError
185 $Value = StandardError($StandardDeviation, $Count);
186
187 Computes the standard error using standard deviation and sample
188 size.
189
190 Standardize
191 $Value = Standardize($Value, $Mean, $StandardDeviation);
192
193 Standardizes the value using mean and standard deviation.
194
195 StandardScores
196 @Values = StandardScores(\@DataArray);
197
198 Computes the standard deviation above the mean for an array of
199 numbers: (x[i] - mean) / (n - 1)
200
201 StandardScoresN
202 @Values = StandardScoresN(\@DataArray);
203
204 Computes the standard deviation above the mean for an array of
205 numbers representing entire population: (x[i] - mean) / n
206
207 Sum
208 $Value = Sum(\@DataArray);
209
210 Compute the sum of an array of numbers.
211
212 SumOfSquares
213 $Value = SumOfSquares(\@DataArray);
214
215 Computes the sum of an array of numbers.
216
217 TrimMean
218 $Value = TrimMean(\@DataArray, $FractionToExclude));
219
220 Computes the mean of an array of numbers by excluding a fraction of
221 numbers from the top and bottom of the data set.
222
223 Variance
224 $Value = Variance(\@DataArray);
225
226 Computes the variance of an array of numbers: SUM( (x[i] - Xmean)^2
227 / (n - 1) )
228
229 VarianceN
230 $Value = Variance(\@DataArray);
231
232 Compute the variance of an array of numbers representing entire
233 population: SUM( (x[i] - Xmean)^2 / n )
234
235 AUTHOR
236 Manish Sud <msud@san.rr.com>
237
238 SEE ALSO
239 Constants.pm, ConversionsUtil.pm, MathUtil.pm
240
241 COPYRIGHT
242 Copyright (C) 2015 Manish Sud. All rights reserved.
243
244 This file is part of MayaChemTools.
245
246 MayaChemTools is free software; you can redistribute it and/or modify it
247 under the terms of the GNU Lesser General Public License as published by
248 the Free Software Foundation; either version 3 of the License, or (at
249 your option) any later version.
250