Estimating detection rates of compact binary inspirals for networks of ground-based gravitational-wave detectors

In a recent paper, Schutz proposed an analytical approximation for simplifying treatment of polarization angle and conveniently evaluating relative detection rates of compact binary inspirals for various networks of ground-based interferometers. We derived relative event rates by strictly handling polarization angle and quantitatively examine validity of Schutz's approximation. The associated error of the approximation is rigorously shown to be less than 1.02\%, irrespective of details of the detector networks.