Single-likelihood estimator (vertical axis; see Eq. (18)) as a function of the observed luminosity distance (horizontal axis). The top, middle, and bottom panels were generated assuming that the GW event is localized in a 1 deg², 10 deg², and 100 deg² sky area. The different lines were generated assuming the four prescriptions of f_rate used in this work and assuming ${\widehat{d}}_L^{\mathrm{thr}}$ = 500 Mpc (we note that such a choice just acts as an overall normalization constant).