ci_lower_bound in plpgsql, from http://www.evanmiller.org/how-not-to-sort-by-average-rating.html

gistfile1.sql

CREATE OR REPLACE FUNCTION ci_lower_bound(integer, integer) RETURNS numeric LANGUAGE plpgsql IMMUTABLE
AS $$
  DECLARE
    up_votes ALIAS FOR $1;
    total_votes ALIAS FOR $2;
    z numeric;
    p_hat numeric;
  BEGIN
    IF total_votes <= 0 OR up_votes < 0 OR up_votes > total_votes THEN
      RETURN 0;
    END IF;

    z := 1.96;
    p_hat := 1.0 * up_votes / total_votes;

    RETURN (p_hat + z * z / (2 * total_votes) - z * sqrt((p_hat * (1 - p_hat) + z * z / (4 * total_votes)) / total_votes)) / (1 + z * z / total_votes);
  END;
$$;