Are all gamma-ray bursts like GRB 980425, GRB 030329, and GRB 031203?

We study the probability that three GRBs (980425, 030329, 031203) are found within z = 0.17, given the luminosity functions consistent with the log N-log S relationship for classical cosmological bursts (i.e., those observed by BATSE). We show that, in order for the probability of these three low-z events to be nonnegligible (thus making it more likely that they belong to the same class of the classical cosmological bursts), the bursts' luminosity function must be a broken power law. By reasoning in analogy with beamed active galactic nuclei, we show that observations are consistent with the expectations if GRB 980425 and GRB 031203 are indeed normal bursts seen sideways. Within this model, no bright burst within z = 0.17 should be observed by a High Energy Transient Explorer-like instrument within the next ≤20 yr.