  As the number of detected gravitational wave sources increase with increasing
sensitivity of the gravitational wave observatories, observing strongly lensed
pair of events will become a real possibility. Lensed GW events will have very
accurately measured time delays, as well as magnification ratios. If the
corresponding lens system can be identified electromagnetically and the
redshifts of the lens and the host galaxy can be measured, such events can be
used to constrain important astrophysical parameters of the lens system. As
most lensing events will have image separations that will be significantly
smaller than the GW event localization uncertainties, it is important that we
develop diagnostics that will aid in the robust identification of such lensed
events. We define a new statistic based on the joint probability of lensing
observables that can be used to discriminate lensed pair of events from the
unlensed ones. To this end, we carry out simulations of lensed GW events to
infer the distribution of the relative time delays, relative magnifications
sub-divided by the type of lensed images. We compare this distribution to a
similar one obtained for random unlensed event pairs. Our improved statistic
can be used to improve the existing ranking approach adopted by the search
pipelines in order to down-select event pairs for joint parameter estimates.
The distributions we obtain can further be used to define more informative
priors in joint parameter estimation analyses for candidate lensed events.
