A quick implementation to generate numbers that roughly comply with Bendford's law.

bendford.rb

module Bendford
  VARIED_DIGITS = 5
  PLACES = [
    [0, *(1..9).map { Math.log10(1.fdiv(_1) + 1) }],
    *(2..VARIED_DIGITS).map do |place|
      (0..9).map do |d|
        (10 ** (place - 2)..((10 ** (place - 1)) - 1)).sum do
          Math.log10(1 + 1.fdiv(10 * _1 + d))
        end
      end
    end
  ]
      
  def self.number(digits:)
    Array.new(digits) do |nth_digit|
      next rand(0..9) if nth_digit >= VARIED_DIGITS
      
      bar = rand
      PLACES.fetch(nth_digit).each_with_index do |chance, winner|
        break winner if chance > bar
        bar -= chance
      end
    end.reduce { |acc, digit| acc * 10 + digit }
  end
end

sample_size = 10_000
digits = 3
example = Array.new(sample_size) { Bendford.number(digits:) }
result = (1..digits).to_h do |n|
  [n, example.map { _1.digits[-n] }.tally]
end
pp result