and derive analytic results which describe the statistics of resonances. Our work probes a fresh area and studies a weak disorder limit which has never been addressed before.

For open systems, instead of studying the scattering matrix in a complex plane we follow an alternative approach where one solves the Schrödinger equation by describing a particle ejected from the system or equivalently with a boundary condition of outgoing waves (Siegert boundary condition [@Siegert]). In this approach one naturally turns up to a problem of solving a non-Hermitian effective Hamiltonian which admits complex eigenvalues $\tilde{{E}}_{\alpha}$ [@GG:00; @KS:06; @KS:08; @HKF:09]. For details of such non-Hermitian effective Hamiltonians, we refer to a recent study [@JF:10] and references therein.

We derive the statistics which describe scattered complex energies of disordered chain around those regular ones which correspond to an open chain without any disorder (clean chain). For instance, we derive average of square of the absolute values of the shifts in complex energies from the regular ones over all realizations of the set of random site energies. Similarly we obtain results for the statistics of real and imaginary parts of those shifts. These results lead to compact expressions for long chains. To show the 