I would lke to review Alpha-quantiles and Ranks with "Empirical Distributions" defined on partial sums of iid. observations discussed in the time continuous version (Brownian Motion). Then revisiting the formulation of classical estimand and estimators for iid observations , described for example in Fillipova's paper, I would like to discuss on what we could do for our partial sums of iid observations in orde to define our non-parametric estimators and estimands. I will be talking only on the ideas, but mathematical proofs will not be provided.