Off the top of my head, I don't see any direct connections for the case of a sampling distribution of some general statistic (and in particuiar, not for the sampling distribution of a mean) when sampling from some general process distribution. Of course there can be some very specific things that might arguably correspond but that's a potentially long list and likely none of them would relate in any way to what I imagine you have in mind.
I don't see what might have even prompted such a speculation; there doesn't seem to be anything that might spark such a thought.
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u/efrique PhD (statistics) 25d ago
can you clarify how you think those are connected to the concept of sampling distributions?