reputation.rb

class Reputation
  class Error < StandardError; end

  def initialize(sample_size:, not_spammy_sample_size:)
    @sample_size = sample_size
    @not_spammy_sample_size = not_spammy_sample_size
  end

  attr_reader :sample_size
  attr_reader :not_spammy_sample_size

  def spammy_sample_size
    sample_size - not_spammy_sample_size
  end

  def reputation
    calculations[0]
  end

  def reputation_lower_bound
    calculations[2].round(4)
  end

  def plus_minus
    calculations[1]
  end

  def minimum_reputation
    minimum_reputation = reputation - plus_minus
    minimum_reputation < 0 ? 0.0 : minimum_reputation
  end

  def maximum_reputation
    maximum_reputation = reputation + plus_minus
    maximum_reputation > 1 ? 1.0 : maximum_reputation
  end

  # Models reputation as the estimated proportion of good items to all items,
  # with a 95% confidence interval, using the normal approximation interval.
  # It returns two values: the estimated reputation and the interval
  # at 95% confidence. See http://bit.ly/2yD5TvJ for more details.
  private def calculations
    @calculations ||= begin
      raise Error.new("sample_size must be ≥ 0") unless sample_size > 0
      raise Error.new("not_spammy_sample_size must be ≥ 0") unless not_spammy_sample_size >= 0
      raise Error.new("sample_size must be ≥ not_spammy_sample_size") unless sample_size >= not_spammy_sample_size

      p_hat = not_spammy_sample_size.to_f / sample_size # p̂ -- estimated proportion
      z_score = 1.95996 # z-score for 95% confidence
      z_squared = z_score * z_score
      plus_minus = z_score * Math.sqrt((p_hat * (1.0 - p_hat)) / sample_size)
      lower_bound = ((2 * sample_size * p_hat) + z_squared - (z_score * Math.sqrt(z_squared + (4 * sample_size * p_hat * (1.0 - p_hat))))) / (2 * (sample_size + z_squared))

      [p_hat, plus_minus, lower_bound]
    end
  end
end