I have been fascinated by Benford for a while, so i finally decided to create a small ruby script that will take a CSV file and compute the frequency distribution of the first digit.
The interesting part is that i haven't used any external library to draw the bar chart, i do everything in the terminal. If you think that these charts would lack of accuracy you will be totally right. I am trying to compensate for this lack of accuracy by computing the margin of error between the result obtained from the data set and Benford's predictions.
https://en.wikipedia.org/wiki/Benford's_law
https://www.youtube.com/watch?v=XXjlR2OK1kM
Here is an example of output:
fenec@ubuntu:~/Desktop/project/benford_s_law$ ruby benford.rb
{"1"=>56.86, "2"=>20.68, "3"=>8.15, "4"=>5.37, "5"=>2.98, "6"=>2.19, "7"=>0.99, "8"=>1.19, "9"=>1.59}
1: ---------------------------------------------------------|result:56.86%-error:88.9%
2: ---------------------|result:20.68%-error:17.43%
3: --------|result:8.15%-error:34.75%
4: -----|result:5.37%-error:44.58%
5: ---|result:2.98%-error:62.37%
6: --|result:2.19%-error:67.26%
7: -|result:0.99%-error:82.93%
8: -|result:1.19%-error:76.76%
9: --|result:1.59%-error:65.28%
20.000000 0.000000 20.000000 ( 22.070408)
fenec@ubuntu:~/Desktop/project/benford_s_law$
You can also display the data in a log graph by passing parameter "log":
$ ruby benford.rb log
{"1"=>56.86, "2"=>20.68, "3"=>8.15, "4"=>5.37, "5"=>2.98, "6"=>2.19, "7"=>0.99, "8"=>1.19, "9"=>1.59}
1: ----------------------------------------------------------|result:5.83 (56.86%).-error:88.9%
2: --------------------------------------------|result:4.37 (20.68%).-error:17.43%
3: ------------------------------|result:3.03 (8.15%).-error:34.75%
4: ------------------------|result:2.42 (5.37%).-error:44.58%
5: ----------------|result:1.58 (2.98%).-error:62.37%
6: -----------|result:1.13 (2.19%).-error:67.26%
7: |result:-0.01 (0.99%).-error:82.93%
8: ---|result:0.25 (1.19%).-error:76.76%
9: -------|result:0.67 (1.59%).-error:65.28%
30.000000 10.000000 40.000000 ( 33.972979)
TODO
-Compute the mean absolute deviation to score the result
-Create a dataset with fibonacci serie and test it