The general term you want to look up here is "L-estimators".

[EDITED to add:] ... Well, kinda. L-estimators are traditionally things you apply to a sample from the distribution, but you're proposing to compute analogous quantities for the distribution itself. But I think this is (except for really pathological cases?) equivalent to taking a really big sample -- e.g., >> n in your example -- and computing the corresponding L-estimator for that sample.