I’m working on a project and I needed to calculate the distribution of the difference between two iid discrete uniform variables (sorry for the long title).

That is, let $I, J$ be two iid discrete uniform variables with support ${1, ldots, k}$. I calculated the distribution of $Z = |I – J|$:

$P(Z = 0) = frac{1}{k}$, $P(Z = y) = frac{2(k-y)}{k^2} forall y in {1, ldots, k-1}$.

I was wondering if such a distribution has a name, so that I can get more info and maybe some results about it.

Thanks a lot.