⟨V/V_max⟩ of the ASKAP and Parkes FRB samples (red and blue squares, respectively) computed accounting for the cosmological terms (K-correction and rate) and the redshifts dispersion. Contours represent the 1-, 2- and 3-σ uncertainties on ⟨V/V_max⟩. A spectral index α = 1.6 is assumed in this figure. Similar plots obtained with other possible values of the spectral index are shown in Fig. 3. The lines show the trends of ⟨V/V_max⟩ as a function of increasing average redshift (i.e. survey depth). The different colours (styles) thick lines show the results of the evolution of ⟨V/V_max⟩ obtained assuming different star formation rates (as labelled, see also Sect. 5).