balsama/benford

A Benford's law distribution and deviation calculator.

Benford Calculator

Benford's Law states that, in many naturally occurring collections of numbers, the leading significant digit is likely to be small. Specifically, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. The same percentages can be extrapolated out to the second and third digits. (After the third digit, all numbers have about the same likelihood of appearing.)

Benford's law

Usage

Include in your project:

$ composer require balsama/benford

Calculating the percentage that digits [0-9] appear in the first three places of a set of numbers.

$set = [123, 1, 707, 2];
$distibution = Balsama\Benford::getBenfordDistrubution($set);
print_r($distibution);
//  [
//      [1] => [0, 50, 25, 0, 0, 0, 0, 25, 0, 0],
//      [2] => [50, 0, 50, 0, 0, 0, 0, 0, 0, 0],
//      [3] => [0, 0, 0, 50, 0, 0, 0, 50, 0, 0],
//  ]

Calculating the deviation from the Benford prediction.

$set = [...]; // A large set of numbers spanning multiple orders of magnitude for best results.
$deviation = Balsama\Benford::getBenfordDeviationScoreFromSet($set);
print $deviation;
// A float. 20 is a good number (meaning likely to be a naturally occurring number set. Use your own data sets to
// determine what a good or bad score is for your purposes.