NAME

SYNOPSIS

    my $stats = Statistics::Benford->new;
    my $diff = $stats->diff(%freq);
    my %diff = $stats->diff(%freq);
    my $signif = $stats->signif(%freq);
    my %signif = $stats->signif(%freq);

DESCRIPTION

METHODS

$stats = Statistics::Benford->new

$stats = Statistics::Benford->new($base, $pos, $len)

Creates a new Statistics::Benford object. The constructor will accept the number base, the position of the significant digit in the number to examine, and the number of digits starting from that position.

The default values are: (10, 0, 1).

%dist = $stats->dist($bool)

%dist = $stats->distribution($bool)

Returns a hash of the expected percentages.

$diff = $stats->diff(%freq)

$diff = $stats->difference(%freq)

%diff = $stats->diff(%freq);

%diff = $stats->difference(%freq)

Given a hash representing the frequency count of the digits in the data to examine, returns the percentage differences of each digit in list context, and the sum of the differences in scalar context.

$diff = $stats->signif(%freq)

$diff = $stats->z(%freq)

%diff = $stats->signif(%freq);

%diff = $stats->z(%freq)

Given a hash representing the frequency count of the digits in the data to examine, returns the z-statistic of each digit in list context, and the average of the z-statistics for all the digits in scalar context.

The z-statistic shows the statistical significance of the difference between the two proportions. Significance takes into account the size of the difference, the expected proportion, and the sample size. Scores above 1.96 are significant at the 0.05 level, and above 2.57 are significant at the 0.01 level.

EXAMPLE

    # Generate a list of numbers approximating a Benford distribution.
    my $max = 10;  # numbers range from 0 to 10
    my @nums = map { ($max / rand($max)) - 1 } (1 .. 1_000);
    my %freq;
    for my $num (@nums) {
        my ($digit) = $num =~ /([1-9])/;  # find first non-zero digit
        $freq{$digit}++;
    }
    my $stats = Statistics::Benford->new(10, 0, 1);
    my $diff = $stats->diff(%freq);
    my $signif = $stats->signif(%freq);

SEE ALSO

<http://www.mathpages.com/home/kmath302/kmath302.htm>

NOTES

Convert non-decimal base digits to decimal representations. For example, to examine the first two digits of a hexadecimal number, like A1B2, take the first two digits 'A1', and convert them to decimal- 161.

The law becomes less accurate when the data set is small.

The law does not apply to data sets which have imposed limitations (e.g. max or min values) or where the numbers are assigned (e.g. ids and phone numbers).

The distribution becomes uniform at the 5th significant digit, i.e. all digits will have the same expected frequency.

It can help to partition the data into subsets for testing, e.g. testing negative and positive values separately.

REQUESTS AND BUGS

SUPPORT

    perldoc Statistics::Benford

You can also look for information at:

• GitHub Source Repository

  <http://github.com/gray/statistics-benford>

• AnnoCPAN: Annotated CPAN documentation

  <http://annocpan.org/dist/Statistics-Benford>

• CPAN Ratings

  <http://cpanratings.perl.org/d/Statistics-Benford>

• RT: CPAN's request tracker

  <http://rt.cpan.org/Public/Dist/Display.html?Name=Statistics-Benford>

• Search CPAN

  <http://search.cpan.org/dist/Statistics-Benford>

COPYRIGHT AND LICENSE

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

AUTHOR