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.