Compact binaries detection rates from gravitational wave
  interferometers: comparison of different procedures
  In this paper we perform a detailed analysis of the effect of various
approximations which have been used in the literature to compute the detection
rates of compact binary coalescences for interferometric gravitational wave
detectors. We evaluate the detection rates for the coalescence of BH-BH, NS-NS,
and BH-NS binaries taking into account their specific statistical properties
obtained from population synthesis models, the cosmic star formation rate
history, and the effects of redshift on the emitted gravitational wave signals.
The results are compared with those obtained with procedures that are based on
different levels of approximations, such as adopting averaged values for the
total mass and symmetric mass ratio for all the systems of a binary population,
using these to compute the horizon distance for individual detectors, or
estimating the coalescence rate density within this distance by its local
value. We show that these approximations introduce a bias which depends not
only on the approximation which is used, but also on the statistical properties
of the considered binary population.
