We study in this paper the behavior of several PRF models, and display their main characteristics. This will lead us to introduce a new heuristic constraint for PRF models, referred to as the Document Frequency (DF) constraint. We then analyze, from a theoretical point of view, state-of-the-art PRF models according to their relation with this constraint. This analysis reveals that the standard mixture model for PRF in the language modeling family does not satisfy the DF constraint. We then conduct a series of experiments in order to see whether the DF constraint is valid or not. To do so, we performed tests with an oracle and a simple family of tf-idf functions based on a prameter k controlling the convexity/concavity of the function. Both the oracle and the results obtained with this family of functions validate the DF constraint.