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We develop a sophisticated model of FRB observations, accounting for the intrinsic cosmological gas distribution and host galaxy contributions, and give the most detailed account yet of observational biases due to burst width, dispersion measure, and the exact telescope beamshape. Our results offer a significant increase in both accuracy and precision beyond those previously obtained. Using results from ASKAP and Parkes, we present our best-fit FRB population parameters in a companion paper. Here, we consider in detail the expected and fitted distributions in redshift, dispersion measure, and signal-to-noise. We estimate that the unlocalised ASKAP FRBs arise from $z<0.5$, with between a third and a half within $z<0.1$. Our predicted source-counts (logN--logS) distribution confirms previous indications of a steepening index near the Parkes detection threshold of $1$,Jy,ms. We find no evidence for a minimum FRB energy, and rule out $E_{rm min} > 10^{38.5}$,erg at 90% C.L. Importantly, we find that above a certain DM, observational biases cause the Macquart (DM--z) relation to become inverted, implying that the highest-DM events detected in the unlocalised Parkes and ASKAP samples are unlikely to be the most distant. We do not expect our quantitative estimates in this region to be accurate until it is directly probed with localised FRBs. Since the cause of this effect is a well-understood observational bias however, it is guaranteed to be present to some degree. Works assuming a 1--1 DM--z relation may therefore derive erroneous results.
We investigate whether current data on the distribution of observed flux densities of Fast Radio Bursts (FRBs) are consistent with a constant source density in Euclidean space. We use the number of FRBs detected in two surveys with different characte
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 thr
In 2007, a very bright radio pulse was identified in the archival data of the Parkes Telescope in Australia, marking the beginning of a new research branch in astrophysics. In 2013, this kind of millisecond bursts with extremely high brightness tempe
Scenario of formation of fast radio bursts (FRBs) is proposed. Just like radio pulsars, sources of FRBs are magnetized neutron stars. Appearance of strong electric field in a magnetosphere of a neutron star is associated with close passage of a dense
Fast radio bursts are mysterious millisecond-duration transients prevalent in the radio sky. Rapid accumulation of data in recent years has facilitated an understanding of the underlying physical mechanisms of these events. Knowledge gained from the