  As first emphasized by Bernard Schutz, there exists a universal distribution
of signal-to-noise ratios for gravitational wave detection. Because
gravitational waves (GWs) are almost impossible to obscure via dust absorption
or other astrophysical processes, the strength of the detected signal is
dictated solely by the emission strength and the distance to the source.
Assuming that the space density of an arbitrary population of GW sources does
not evolve, we show explicitly that the distribution of detected
signal-to-noise (SNR) values depends solely on the detection threshold; it is
independent of the detector network (interferometer or pulsar timing array),
the individual detector noise curves (initial or Advanced LIGO), the nature of
the GW sources (compact binary coalescence, supernova, or some other discrete
source), and the distributions of source variables (only non-spinning neutron
stars of mass exactly $1.4\,M_\odot$ or a complicated distribution of masses
and spins). We derive the SNR distribution for each individual detector within
a network as a function of the relative detector orientations and
sensitivities. While most detections will have SNR near the detection
threshold, there will be a tail of events to higher SNR. We derive the SNR
distribution of the loudest (highest SNR) events in any given sample of
detections. We find that the median SNR of the loudest out of the first four
events should have an $\mbox{SNR}=22$ (for a threshold of 12, appropriate for
the Advanced LIGO/Virgo network), increasing to a median value for the loudest
SNR of 47 for 40 detections. We expect these loudest events to provide
particularly powerful constraints on their source parameters, and they will
play an important role in extracting astrophysics from gravitational wave
sources. These distributions also offer an important internal calibration of
the response of the GW detector networks.
