<1.0$, which is significantly different from the value of $\alpha=1.5$ expected for a non-evolving population in Euclidean space. We reject $\alpha=1.5$ with $>99\%$ confidence.\
We have evaluated the robustness of our results against survey incompleteness at faint fluence levels where the bursts are predominantly expected to be single-beam events. [@keane2015] studied survey incompleteness effects in simulations and found that up to 22% of the bursts can be missed for a Euclidean distribution of FRB fluences ($\alpha=1.5$). This corresponds to 5 missed detections. We recomputed the bounds on $\alpha$ for a hypothetical scenario where 5 more FRBs are discovered at Parkes. We assume that all 5 are single-beam detections, 3 of which are detected in an inner ring beam and the remaining 2 in an outer ring beam. The constraint on $\alpha$ for this hypothetical scenario is $0.58<\alpha<1.06$ at 90% confidence, which clearly demonstrates the robustness and unbiased nature of our bounds on $\alpha$ against survey incompleteness. In addition, our results are robust to variations in intrinsic burst properties since they do not affect the *fraction* of multiple-beam detections as considered here.\
We finally note that our bounds are, as expected, highly sensitive to the number of multiple-beam detections. For instance, 