  We examine how the various observable statistical properties of the FRB
population relate back to their fundamental physical properties in a model
independent manner. We analyse the flux density and fluence distributions of
Fast Radio Bursts (FRBs) as a tool to investigate their luminosity distance
distribution and the evolution of their prevalence throughout cosmic history.
We examine in detail particular scenarios in which the burst population follows
some power of the cosmic star formation rate. FRBs present an important
additional measurable over source counts of existing cosmological populations,
namely the dispersion measure. Based on the known redshift of FRB121102 (the
repeater) we expect at least 50% of the dispersion measure to be attributable
to the inter-galactic medium and hence it can be used as a proxy for distance.
We develop the framework to interpret the dispersion measure distribution, and
investigate how the effect of Helium reionization in the intergalactic medium
is evident in this distribution. Examination of existing data suggests that the
FRB luminosity function is flatter than a critical slope, making FRBs easily
detectable to large distances; in this regime the reduction in flux density
with distance is outweighed by the increase in the number of bright bursts
within the search volume.
