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tokens: Parkes and ASKAP DM histograms with corresponding modelled DM distributions, d R F /d DM , where R F is the total differential (fluence) event rate in the observer’s frame (d R F /d DM has units of events s −1 (pc cm −3 ) −1 sr −1 ). Table 2. Symbol definitions relevant to the ME 2018 model utilized herein with some minor notational changes and extensions. The DM distribution, for fluences above a minimum survey fluence limit, is dependent upon a number of factors including the underlying redshift distribution of the population (relating to the evolutionary history) and the mean DM gradient, , for an assumed homogeneous IGM. These are dependent upon the source energy distribution function, characterized by the source minimum and maximum energies E min and E max , respectively, the energy power-law index and the spectral index (Macquart Ekers 2018b ). Throughout this work we utilize a ΛCDM universe with cosmological parameters and equations consistent with the Planck Collaboration XVI ( 2014 ) 3 and Hogg ( 1999 ), and symbol definitions of the ME 2018 model with some minor notational changes and extensions as summarized in Table 2 . The FRB redshift and DM distributions, in a survey of limiting fluence, are respectively given by equations ( 2 ) ( 3 ) and where the minimum and maximum of the source energy is related, respectively, to the corresponding minimum and maximum fluence via . Here, ψ n ( z ) and represent redshift evolution (Madau Dickinson 2014 ), via equation ( 4 ), and the mean DM of an homogeneous IGM (Ioka 2003 ; Inoue 2004 ), via equation ( 5 ), respectively and Whilst the underlying redshift distribution of the FRB population is unknown, we follow Macquart Ekers ( 2018b ) and adopt the Madau Dickinson ( 2014 ) formalism for the cosmic star formation history of the Universe. Equation ( 4 ) accounts for the redshift evolution of the rate density for a progenitor population abundance, governed by stellar processes throughout cosmic history, via the relation ψ n ( z )∝Ψ n ( z ). Here, Ψ represents the cosmic star formation rate (CSFR) per comoving volume and the event rate per comoving volume, ψ n ( z ), is related via a power-law index, n (Macquart Ekers 2018b ). We specifically consider three cases: (i) ψ 0 ( z ) – no redshift evolution; (ii) ψ 1 ( z ) – redshift evolution being linearly proportional to the CSFR; and (iii) ψ 2 ( z ) – redshift evolution being quadratically proportional to the CSFR. The case of ψ 0 ( z ) = 1 represents a constant event rate per comoving volume and ψ 2 ( z ) represents a rapidly evolving population. Furthermore, throughout this work, we set the ionized fraction of Hydrogen and Helium to X e, H = 1 for z 8 and X e, He = 1 for z 2.5, respectively, and zero otherwise, and take α to refer to the spectral index of the burst fluence unless specifically noted otherwise. The dimensionless Hubble parameter, E ( z ), permits the Hubble parameter for an arbitrary redshift, H ( z ), to be determined given the