Notation for sampling specific number of samples from distribution

Question

I am in the process of writing a scientific paper. At a certain point I want to mention a sampling operation, namely that a variable hereafter called X is a sample obtained from a distribution T. Normally I would show this as X ~ p(T). However in my case it is very important to explicitly mention the size of that sample in order to highlight the fact that I am obtaining exactly k samples from that distribution. I thought of incorporating that in the distribution and write X ~ p(T; k) but this feels wrong: the distribution is the same regardless of how many samples I drew from it. I could also write X ~ p(T) so that |X| = k or perhaps X = {x_i ~ p(T) for i in [0, k)} but I was hoping for a more succinct notation if one exists.

Answer 1

This would be a fairly standard way to represent a random sample from $T$: $\mathbf X_k=\{X_1,\dots,X_k\}$ with $X_j\overset{\text{i.i.d.}}{\sim} T$.

None of the other notations you suggested are in common usage and will almost indefinitely confuse a reader unless explicitly defined.

Another slightly more compact option would be: $\mathbf X_k=\{X_j\}_{j=1}^k$ with $X_j\overset{\text{i.i.d.}}{\sim} T$.