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

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