LogN-LogS distribution of the simulated sources. A constant source density of 8 × 10⁻⁹ Mpc⁻³ (the effective density of BL Lac objects; see Sect. 3) corresponds to 1.2 × 10⁴ sources within redshift z = 4. The flux on the x-axis is given as the expected number of detected neutrino events and is normalized such that ten events are expected from the complete population. Since all sources are equally luminous, the flux can be converted to the source distance shown on the upper x-axis. For nearby sources, the LogN-LogS distribution is proportional to S^−3/2 as expected for an Euclidean universe. The probability distributions in the lower panel show from which sources the detection of one, two, or three events is most likely expected. The dashed lines indicate the median source flux and the colored bands in the upper panel include 90% of the probability distributions for one and three detected events. In the adopted example, a source detected with a single event is most likely located at a distance between 0.5 and 20 Gpc and its flux can be as small as 10⁻⁴ expected events.