Can Repeating and Nonrepeating Fast Radio Bursts Be Drawn from the Same Population?

Do all fast radio burst (FRB) sources repeat? We present evidence that FRB sources follow a Zipf-like distribution, in which the number density of sources is approximately inversely proportional to their burst rate above a fixed energy threshold—even though both the burst rate and number density span many orders of magnitude individually. We introduce a model-independent framework that predicts the distribution of observed fluences and distances, and the repetition rates of an FRB population based on an assumed burst rate distribution per source. Using parameters derived directly from observations, this framework simultaneously explains several key features of the FRB population: (i) the observed ratio of repeaters to apparent nonrepeaters; (ii) the much lower ratio of apparent nonrepeaters to the total number of soft gamma repeater (SGR) sources within the observable Universe; and (iii) the slightly smaller average distances of known repeaters compared to nonrepeaters. We further explore how survey parameters, such as radio sensitivity and observation time, influence these statistics. Notably, we find that the fraction of repeaters rises only mildly with improved sensitivity or longer exposure. This weak dependence could be misinterpreted as evidence that not all FRBs repeat. Overall, our results support the idea that a single population—likely magnetars—can account for the full observed diversity of FRB activity, from very inactive FRB sources like SGR 1935+2154 to the most active repeaters.