We formulate Gaussian and circular random-matrix models representing a
coupled system consisting of an absorbing and an amplifying resonator, which
are mutually related by a generalized time-reversal symmetry. Motivated by
optical realizations of such systems we consider a PT or a PTT' time-reversal
symmetry, which impose different constraints on magneto-optical effects, and
then focus on five common settings. For each of these, we determine the
eigenvalue distribution in the complex plane in the short-wavelength limit,
which reveals that the fraction of real eigenvalues among all eigenvalues in the
spectrum vanishes if all classical scales are kept fixed. Numerically, we find that
the transition from real to complex eigenvalues in the various ensembles display
a different dependence on the coupling strength between the two resonators.
These differences can be linked to the level spacing statistics in the Hermitian
limit of the considered models.