PHP - Generating random numbers within an interval with respect to the mode X

I am trying to generate random numbers that their mode is equal to X (any real number). As a way of illustration, I expect a function whose header is rand(int min, int max, int mode), and when I call it with the following parameters rand(min: 1, max: 6, mode: 4) generates the following:

(1,2,4,4,4,5,3) // not exact, but similar

I am searching for an optimized way of doing so (although doing it manually would be the worst case, I am out of thoughts).

I have checked mt_rand(), rand, and other random generation functions, but have not found what I am looking for.

Any suggests?