Fast radio bursts: search sensitivities and completeness

In this paper we identify some sub-optimal performance in algorithms that search for fast radio bursts (FRBs), which can reduce the cosmological volume probed by over 20 per cent, and result in missed discoveries and incorrect flux density and sky rate determinations. Recalculating parameters for all of the FRBs discovered with the Parkes telescope (i.e. all of the reported FRBs bar one), we find some inconsistencies with previously determined values, e.g. FRB 010125 was approximately twice as bright as previously reported. We describe some incompleteness factors not previously considered which are important in determining accurate population statistics, e.g. accounting for fluence incompleteness the Thornton et al. all-sky rate can be re-phrased as similar to 2500 FRBs per sky per day above a 1.4-GHz fluence of similar to 2 Jy ms. Finally we make data for the FRBs easily available, along with software to analyse these.