Random values with non-uniform distribution

Question

I want a random number generator with non-uniform distribution, ie:

// prints 0 with 0.1 probability, and 1 with 0.9 probability
echo probRandom(array(10, 90         


        

Answer 1

If you know the sum of all elements in $probs, you can do this without preprocessing.

Like so:

$max = sum($probs);
$r = rand(0,$max-1);
$tot = 0;
for ($i = 0; $i < length($probs); $i++) {
    $tot += $probs[$i];
    if ($r < $tot) {
        return $i;
    }
}

This will do what you want in O(N) time, where N is the length of the array. This is a firm lower bound on the algorithmic runtime of such an algorithm, as each element in the input must be considered.

The probability a given index $i is selected is $probs[$i]/sum($probs), given that the rand function returns independent uniformly distributed integers in the given range.