dropping the 4-beam event FRB010724 [@lorimer2007] from our calculations revises the constraint to $0.88<\alpha<1.52$. This is still marginally inconsistent with a Euclidean population.

![Posterior probability distribution of $\alpha$ given the 16 Parkes detections (solid red curve), conditional upon FRBs being far-field events with integral source counts given by $N(>{\mathcal{F}_{\rm obs}}) \propto {\mathcal{F}_{\rm obs}}^{-\alpha}$. The green dashed curve is the corresponding cumulative distribution function, and the blue dotted line is its complement. The posterior bounds on $\alpha$ are $0.52<\alpha<1.0$ at 90% confidence. \[fig:alpha\_modsel\]](alpha_modelsel.pdf){width="\linewidth"}

Multi-telescope detection statistics {#sec:alpha_mt}
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Several telescopes have been searching for FRBs, each with their own sensitivities and survey volumes. The number of expected FRB detections from a given telescope depends on the nature of the source count distribution (log$N$-log$F$ curve) for FRBs. For instance, larger dishes have more collecting area but narrower fields of view. They are thus best suited to detecting faint events, and are favored by a steep log$N$-log$F$ slope that implies a large number of faint objects. Shallower log$N$-log$F$ distributions, on the other hand, yield large numbers of bright events which makes the telescope sensitivity less relevant than the field of view in achieving greater detection rates. Hence, detections, or the lack thereof, from 