Abstract
Currently, fast radio bursts (FRBs) have become a very active field in astronomy and cosmology. However, the origin of FRBs is still unknown to date. The studies on the intrinsic FRB distributions might help us to reveal the possible origins of FRBs, and improve the simulations for FRB cosmology. Recently, the first CHIME/FRB catalog of 536 events was released. Such a large uniform sample of FRBs detected by a single telescope is very valuable to test the FRB distributions. Later, it has been claimed that the FRB distribution model tracking the cosmic star formation history (SFH) was rejected by the first CHIME/FRB catalog. In the present work, we consider some empirical FRB distribution models, and find that many of them can be fully consistent with the CHIME/FRB observational data for some suitable model parameters. Notice that a suppressed evolution with respect to SFH is commonly found for FRBs. In particular, we independently confirm that the FRB distribution model tracking SFH can be rejected at very high confidence. On the other hand, all the "successful" models effectively require a certain degree of "delay" with respect to SFH. These results might shed light on the origin of FRBs and FRB cosmology.