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Although there has recently been tremendous progress in studies of fast radiobursts (FRBs), the nature of their progenitors remains a mystery. We study thefluence and dispersion measure (DM) distributions of the ASKAP sample to betterunderstand their energetics and statistics. We first consider a simplifiedmodel of a power-law volumetric rate per unit isotropic energy dN/dE ~E^{-gamma} with a maximum energy E_max in a uniform Euclidean Universe. Thisprovides analytic insights for what can be learnt from these distributions. Wefind that the observed cumulative DM distribution scales as N(>DM) ~DM^{5-2*gamma} (for gamma > 1) until a maximum value DM_max above which burstsnear E_max fall below the fluence threshold of a given telescope. Comparingthis model with the observed fluence and DM distributions, we find a reasonablefit for gamma ~ 1.7 and E_max ~ 10^{33} erg/Hz. We then carry out a fullBayesian analysis based on a Schechter rate function with cosmological factor.We find roughly consistent results with our analytical approach, although withlarge errors on the inferred parameters due to the small sample size. Thepower-law index and the maximum energy are constrained to be gamma = 1.6 +/-0.3 and log(E_max) [erg/Hz] = 34.1 +1.1 -0.7 (68% confidence), respectively.From the survey exposure time, we further infer a cumulative local volumetricrate of log N(E > 10^{32} erg/Hz) [Gpc^{-3} yr^{-1}] = 2.6 +/- 0.4 (68%confidence). The methods presented here will be useful for the much larger FRBsamples expected in the near future to study their distributions, energetics,and rates.

Implications from ASKAP Fast Radio Burst Statistics