The fluence distribution of the Fast Radio Burst ( FRB ) population ( the ‘ ‘ source counts ’ ’ distribution , N ( > F ) \propto F ^ { \alpha } ) , is a crucial diagnostic of its distance distribution , and hence the progenitor evolutionary history .
We critically reanalyse current estimates of the FRB source counts distribution .
We demonstrate that the Lorimer burst ( FRB 010724 ) is subject to discovery bias , and should be excluded from all statistical studies of the population .
We re-examine the evidence for flat , \alpha > -1 , source counts estimates based on the ratio of single-beam to multiple-beam detections with the Parkes multi-beam receiver , and show that current data implies only a very weak constraint of \alpha \lesssim - 1.3 .
A maximum likelihood analysis applied to the portion of the Parkes FRB population detected above the observational completeness fluence of 2 Jy ms yields \alpha = -2.6 _ { -1.3 } ^ { +0.7 } .
Uncertainties in the location of each FRB within the Parkes beam render estimates of the Parkes event rate uncertain in both normalising survey area and the estimated post-beam-corrected completeness fluence ; this uncertainty needs to be accounted for when comparing the event rate against event rates measured at other telescopes .