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package Statistics::SerialCorrelation; |
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use base 'Exporter'; |
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@EXPORT_OK = qw(serialcorrelation); |
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$VERSION = '1.1'; |
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use strict; |
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use warnings; |
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=head1 NAME |
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Statistics::SerialCorrelation - calculate the serial correlation |
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co-efficient for an array |
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=head1 SYNOPSIS |
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use Statistics::SerialCorrelation; |
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print Statistics::SerialCorrelation::serialcorrelation(1..6); |
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Or if you don't mind polluting your namespace, you may import the |
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serialcorrelation function like so: |
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use Statistics::SerialCorrelation 'serialcorrelation'; |
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=head1 DESCRIPTION |
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This module does just one thing, it calculates Serial Correlation |
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Co-efficients, which are a measure of how predictable a series of |
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values is. For example, the sequence: |
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1 2 3 4 5 6 7 8 9 10 |
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is very predictable, and will have a high serial correlation |
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co-efficient. The sequence |
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10 1 3 2 6 7 7 9 2 |
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is less predictable and so has a correlation co-efficient nearer 0. |
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In general, random data has a co-efficient close to zero, highly-ordered |
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data doesn't. Note that the co-efficient may be negative. |
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There is just one function. |
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=over 4 |
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=item serialcorrelation |
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This takes either a list of numbers or an array reference. If given |
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an array reference, this is first turned into an array. It then |
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calculates the correlation co-efficient and returns it. |
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See your copy of Knuth for the formula. |
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=back |
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=cut |
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sub serialcorrelation { |
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my @U = @_; |
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@U = @{$U[0]} if(ref($U[0]) =~ /^ARRAY/); |
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my $n = $#U + 1; |
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my($sum_of_products_of_pairs, $sum_of_squares, $sum) = ( |
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$U[$n - 1] * $U[0], |
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$U[$n - 1] * $U[$n - 1], |
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$U[$n - 1] |
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); |
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foreach(0 .. $n - 2) { |
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$sum_of_products_of_pairs += $U[$_] * $U[$_ + 1]; |
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$sum_of_squares += $U[$_] * $U[$_]; |
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$sum += $U[$_] |
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} |
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return undef if($n * $sum_of_squares == $sum * $sum); |
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(($n * $sum_of_products_of_pairs) - ($sum * $sum)) / |
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(($n * $sum_of_squares) - ($sum * $sum)); |
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} |
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=head1 BUGS |
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To avoid divide-by-zero errors, we return undef if the square of the sum of |
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your values is equal to the number of values multiplied by the sum of the |
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squares of the values. undef was chosen because it will never otherwise be |
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returned and so you can easily detected. |
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The results are not particularly meaningful for small data sets. |
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No other bugs are known, but if you find any please let me know, and send a |
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test case. |
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=head1 FEEDBACK |
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I welcome feedback about my code, including constructive criticism. |
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=head1 AUTHOR |
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David Cantrell EFE |
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=head1 COPYRIGHT |
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105
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Copyright 2003 David Cantrell |
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This module is free-as-in-speech software, and may be used, distributed, |
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and modified under the same terms as Perl itself. |
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110
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=cut |
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112
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1; |