creating random numbers that favor smaller numbers?

Question

say i generated a set of random numbers and put them into an array, (pre-sorted for simplicity) i'll use javascript to show the math: var vals = new Array(0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,...,10000); then in a loop, i created a random number to serve as an index: for(i=0;i<10000;i++){ var random_index = Math.floor(Math.random() * 10000); var result = vals[random_index]; } if you looked at this output on any kind of graph, the results (with enough iterations through that loop, will look pretty random and balanced) what I want, is for the results of each access to favor smaller numbers, which incidentally here is array elements with a lower index. for a visual example, imagine you're trying to plot on a map where the fragments of a firework fell. most of those fragments would fall randomly within a vicinity but have a heavier concentration towards the middle. that's a bit of an over-complicated example since it's taking another dimension into account and uses physics to achieve the result, but it's the same principal. what operation should i perform on the random_index variable to make it 'favor' smaller numbers?

Answer 1

The random number generator is supposed to be uniformly distributed or obey the uniform distribution; that is, each number is equally likely to be selected, so using the random number generator is theoretically a bad idea.

The normal distribution tends to FAVOR the mean average. In fact by empirical rule, 2/3 of the data lie within 1 standard deviation of the mean average. In your fireworks example, the debris would tend to cluster around the launch pad with fragments in fewer amounts spreading outward.

So one option would be to convert your data to z-scores and throw away anybody between -1 and 1.

That would leave you with 1/6 of them being "SMALL" and 1/6 of them being "LARGE"

If you want all 1/3 of them, just change the sign, as the bell curve is symmetric anyway.

So what you're getting is z = (-infinity,-1) U (1,infinity)

You can hijack the random number generator and create a hashed function like this:

if 0 < random # < 25 ---> maps to 1

25 < random # < 50 -----> maps to 2

50 < random # < 75 -----> maps to 3

70 < random # < 100 ----> maps to 4

that way you will always get a "SMALL" number