Ranking algorithm - Lower bound of Wilson score confidence interval for a Bernoulli parameter All implementations use 95% probability.

description.md

Ranking algorithm

Lower bound of Wilson score confidence interval for a Bernoulli parameter

All implementations use 95% probability.

pos is the number of positive votes, n is the total number of votes.

Source

main.clj

(ns ranking.core
  (:use clojure.contrib.math)
  (:gen-class))

(def z 1.96)

(defn ci
  [pos n]
  (let [phat (/ (* 1.0 pos) n)]
    (/ (- (+ phat
          (/ (* z z)
             (* n 2)))
          (* z
             (sqrt (/ (+ (* phat
                            (- 1 phat))
                         (/ (* z z)
                            (* 4 n)))
                       n))))
       (+ 1 (/ (* z z) n)))))

(defn -main
  [& args]
  (println (ci 600 1000))
  (println (ci 5500 10000)))

main.js

function ci(pos, n) {
    var z, phat;
    
    z = 1.96;
    phat = 1 * pos / n;

    return (phat + z*z/(2*n) - z * Math.sqrt((phat*(1-phat)+z*z/(4*n))/n))/(1+z*z/n);

}

console.log(ci(600, 1000));
console.log(ci(5500, 10000));

main.py

import math


def ci(pos, n):
    z = 1.96
    phat = 1.0 * pos / n

    return (phat + z*z/(2*n) - z * math.sqrt((phat*(1-phat)+z*z/(4*n))/n))/(1+z*z/n)


print ci(600, 1000)
print ci(5500, 10000)