Interpreting the distributions of FRB observables

Fast radio bursts (FRBs) are short-duration radio transients of unknown origin. Thus far, they have been blindly detected at millisecond timescales with dispersion measures (DMs) between 110--2600\,pc\,cm$^{-3}$. However, the observed pulse width, DM, and even brightness distributions depend strongly on the time and frequency resolution of the detection instrument. Spectral and temporal resolution also significantly affect FRB detection rates, similar to beam size and system-equivalent flux density (SEFD). I discuss the interplay between underlying FRB properties and instrumental response, and provide a generic formalism for calculating the \textit{observed} distributions of parameters given an intrinsic FRB distribution, focusing on pulse width and DM. I argue that if there exist many FRBs of duration $<<$\,1\,ms (as with giant pulses from Galactic pulsars) or events with high DM, they are being missed due to the deleterious effects of smearing. I outline how to optimise spectral and temporal resolution for FRB surveys that are throughput-limited. I also investigate how such effects may have been imprinted on the distributions of FRBs at real telescopes, like the different observed DMs at ASKAP and Parkes. Finally, I discuss the impact of intrinsic correlations between FRB parameters on detection statistics.