Unbalanced random number generator

Question

I have to pick an element from an ascending array. Smaller elements are considered better. So if I pick an element from the beginning of the array it's considered a better choice. But at the same time I don't want the choice to be deterministic and always the same element. So I'm looking for

a random numbers generator that produces numbers in range [0, n], but the smaller the number is, the more chance of it being produced.

This came to my mind:

num = n;
while(/*the more iteration the more chance for smaller numbers*/)
  num = rand()%num;

I was wondering if anyone had a better solution.
I did look at some similar questions but they have details about random number generation generally. I'm looking for a solution to this specific type of random number generation, either an algorithm or a library that provides it.

Answer 1

Generate a Random number, say x, between [0,n) and then generate another Random floating point number, say y, between [0,1]. Then raise x to the power of y and use floor function, you'll get your number.

int cust(int n)
{
  int x;
  double y, temp;
  x = rand() % n;
  y = (double)rand()/(double)RAND_MAX;
  temp = pow((double) x, y);
  temp = floor(temp);
  return (int)temp;
}

Update: Here are some sample results of calling the above function 10 times, with n = 10, 20 and 30.

2 5 1 0 1 0 1 4 1 0

1 2 4 1 1 2 3 5 17 6

1 19 2 1 2 20 5 1 6 6

Answer 2

Simple ad-hoc approach that came to my mind is to use standard random generators, but duplicate indices. So in the array:

0, 0, 0, 1, 1, 2, 3

odds are good that smaller element will be taken.
I dont' know exactly what do you need. You can also define your own distribution or maybe use some random number generation libraries. But suggested approach is simple and easy to configure.
UPDATE2: You don't have to generate array explicitly. For array of size 1000, you can generate random number from interval: [0,1000000] and then configure your own distribution of selected values: say, intervals of length 1200 for smaller values (0-500) and intervals of length 800 for larger (500-1000). The main point that this way you can easily configure the probability and you don't have to re-implement random number generator.