[PHP] 5 Star Rating - Lower bound of Wilson score confidence interval for a Bernoulli parameter

wilson.php

<?php

/*
|--------------------------------------------------------------------------
| 5 Star Rating
|--------------------------------------------------------------------------
|
| Lower bound of Wilson score confidence interval for a Bernoulli parameter (0.9604)
|
| See: 
|  * http://www.evanmiller.org/how-not-to-sort-by-average-rating.html
|  * https://gist.github.com/richardkundl/2950196
|  * https://onextrapixel.com/how-to-build-a-5-star-rating-system-with-wilson-interval-in-mysql/
|
*/


function score($positive, $negative) {
    return ((($positive + 1.9208) / ($positive + $negative) - 1.96 * sqrt((($positive * $negative) / ($positive + $negative)) + 0.9604) / ($positive + $negative)) / (1 + 3.8416 / ($positive + $negative)));
}

function fiveStarRating($one, $two, $three, $four, $five) {
    $positive = $two * 0.25 + $three * 0.5 + $four * 0.75 + $five;
    $negative = $one + $two * 0.75 + $three * 0.5 + $four * 0.25;

    return score($positive, $negative);
}

function fiveStarRatingAverage($avg, $total)
{
    $positive = ($avg * $total - $total) / 4;
    $negative = $total - $positive;

    return score($positive, $negative);
}

// Examples

echo fiveStarRating(10, 1, 2, 6, 90);     // 0.80390178246001
echo fiveStarRating(80, 1, 2, 6, 90);     // 0.46188074417216
echo fiveStarRating( 0, 1, 2, 6, 0 );     // 0.33136280289755
echo fiveStarRating(10, 1, 2, 0, 2 );     // 0.079648861762752

echo fiveStarRatingAverage(4.8000001907349, 10);        // 0.65545605272928