As pointed out by @law2015, the source count assumed here (Equation \[eqn:eventrate\]) has been estimated based on average burst properties such as DMs, intrinsic widths, scattering timescales etc. The distribution functions for these properties are not well known. In addition, the constraints on $\alpha$ are somewhat degenerate with the over-all normalization of the all-sky FRB rate[@oppermann2016]. To gauge the sensitivity of our constraints to such effects in a simplified manner, we have recomputed the confidence interval for $\alpha$ for a selection of cases. We have assumed the fiducial values for DM, $\tau_{\rm FRB}$ and the normalization of FRB source counts of 780 pc cm$^{-3}$, 3 ms, and $1.2\times 10^4$ events above a fluence of 1.8 Jy ms per day respectively. In each case, we vary one of these three parameters by 100% while fixing the other to their fiducial values.

-   Consider the number of events per day above a fluence of 1.8 Jy ms to be $0.6\times10^4$ or $2.4\times 10^4$ (see Equation \[eqn:eventrate\]). The respective constraints on $\alpha$ are $0.63<\alpha<1.16$ and $0.71<\alpha<0.99$.

-   Consider the mean FRB width to be $\tau_{\rm FRB}=1.5$ ms or $\tau_{\rm FRB}=6$ ms. The respective constraints on $\alpha$ are $0.66<\alpha<0.99$ and $0.68<\alpha<1.15$.

-   Consider the 