The slope of the source-count distribution of fast radio burst ( FRB ) fluences , \alpha , has been estimated using a variety of methods .
Hampering all attempts have been the low number of detected FRBs , and the difficulty of defining a completeness threshold for FRB surveys .
In this work , we extend maximum-likelihood methods for estimating \alpha , using detected and threshold signal-to-noise ratios applied to all FRBs in a sample without regard to a completeness threshold .
Using this method with FRBs detected by the Parkes radio telescope , we find \alpha = -1.18 \pm 0.24 ( 68 % confidence interval , C.I .
) , i.e .
consistent with a non-evolving Euclidean distribution ( \alpha = -1.5 ) .
Applying these methods to the Australian Square Kilometre Array Pathfinder ( ASKAP ) Commensal Real-time ASKAP Fast Transients ( CRAFT ) FRB survey finds \alpha = -2.2 \pm 0.47 ( 68 % C.I . ) .
A full maximum-likelihood estimate finds an inconsistency with the Parkes rate with a p-value of 0.86 % ( 2.6 \sigma ) .
If not due to statistical fluctuations or biases in Parkes data , this is the first evidence for deviations from a pure power law in the integral source-count distribution of FRBs .
It is consistent with a steepening of the integral source-count distribution in the fluence range 5–40 Jy ms , for instance due to a cosmological population of FRB progenitors evolving more rapidly than the star-formation rate , and peaking in the redshift range 1–3 .