  We present a generic formalism to constrain the cosmic rate density history
and the source luminosity function of FRB progenitors from the statistical
properties of the apparent flux density of non-repeating FRBs detected with
Parkes. We include the pulse multipath propagation effects to evaluate the flux
density distribution for a generalised spatial density model and luminosity
function. We perform simulations to investigate the effects of the telescope
beam pattern and temporal resolution on the observed flux density. We find that
the FRB progenitors are likely to be younger stars with a relatively flat
energy spectrum and host galaxy DM contribution similar to the MW. Our analysis
can be extended to larger FRB samples detected with multiple surveys to place
stronger constraints on the FRB progenitor properties.
