Probability distributions of FRBs as functions of redshift for different models. Left panel: probability density functions (PDFs) of the intrinsic FRB population versus redshift, for the Euclidean, SFR and delayed SFR models with three delay times. The redshift range [0, 1.5] is used in our simulation. For information, we also show the region [1.5, 2.5], gray shaded, such that the shift of the SFR peak is visible between the models. Right panel: simulated observed FRB population PDFs against redshift, for the same models. The mean redshift ⟨z⟩ for the different models are marked by the dashed vertical lines. An unfilled zoomed-in view of the redshift range [0, 0.2] is also shown.