BenfordsLaw

2 พ.ค. 2023

Library "BenfordsLaw"
Methods to deal with Benford's law which states that a distribution of first and higher order digits
of numerical strings has a characteristic pattern.
"Benford's law is an observation about the leading digits of the numbers found in real-world data sets.
Intuitively, one might expect that the leading digits of these numbers would be uniformly distributed so that
each of the digits from 1 to 9 is equally likely to appear. In fact, it is often the case that 1 occurs more
frequently than 2, 2 more frequently than 3, and so on. This observation is a simplified version of Benford's law.
More precisely, the law gives a prediction of the frequency of leading digits using base-10 logarithms that
predicts specific frequencies which decrease as the digits increase from 1 to 9." ~(2)
---
reference:
- 1: en.wikipedia.org/wiki/Benford's_law
- 2: brilliant.org/wiki/benfords-law/
- 4: github.com/vineettanna/Benfords-Law/tree/master

cumsum_difference(a, b)
  Calculate the cumulative sum difference of two arrays of same size.
  Parameters:
    a (float[]): `array<float>` List of values.
    b (float[]): `array<float>` List of values.
  Returns: List with CumSum Difference between arrays.

fractional_int(number)
  Transform a floating number including its fractional part to integer form ex:. `1.2345 -> 12345`.
  Parameters:
    number (float): `float` The number to transform.
  Returns: Transformed number.

split_to_digits(number, reverse)
  Transforms a integer number into a list of its digits.
  Parameters:
    number (int): `int` Number to transform.
    reverse (bool): `bool` `default=true`, Reverse the order of the digits, if true, last will be first.
  Returns: Transformed number digits list.

digit_in(number, digit)
  Digit at index.
  Parameters:
    number (int): `int` Number to parse.
    digit (int): `int` `default=0`, Index of digit.
  Returns: Digit found at the index.

digits_from(data, dindex)
  Process a list of `int` values and get the list of digits.
  Parameters:
    data (int[]): `array<int>` List of numbers.
    dindex (int): `int` `default=0`, Index of digit.
  Returns: List of digits at the index.

digit_counters(digits)
  Score digits.
  Parameters:
    digits (int[]): `array<int>` List of digits.
  Returns: List of counters per digit (1-9).

digit_distribution(counters)
  Calculates the frequency distribution based on counters provided.
  Parameters:
    counters (int[]): `array<int>` List of counters, must have size(9).
  Returns: Distribution of the frequency of the digits.

digit_p(digit)
  Expected probability for digit according to Benford.
  Parameters:
    digit (int): `int` Digit number reference in range `1 -> 9`.
  Returns: Probability of digit according to Benford's law.

benfords_distribution()
  Calculated Expected distribution per digit according to Benford's Law.
  Returns: List with the expected distribution.

benfords_distribution_aprox()
  Aproximate Expected distribution per digit according to Benford's Law.
  Returns: List with the expected distribution.

test_benfords(digits, calculate_benfords)
  Tests Benford's Law on provided list of digits.
  Parameters:
    digits (int[]): `array<int>` List of digits.
    calculate_benfords (bool)
  Returns: Tuple with:
- Counters: Score of each digit.
- Sample distribution: Frequency for each digit.
- Expected distribution: Expected frequency according to Benford's.
- Cumulative Sum of difference:

to_table(digits, _text_color, _border_color, _frame_color)
  Parameters:
    digits (int[])
    _text_color (color)
    _border_color (color)
    _frame_color (color)

15 มิ.ย. 2023

เอกสารเผยแพร่

v2 minor update.

30 มิ.ย. 2023

เอกสารเผยแพร่

Fix logger version.