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We investigate the statistical properties of the complexness parameter whichcharacterizes uniquely complexness (biorthogonality) of resonance eigenstatesof open chaotic systems. Specifying to the regime of isolated resonances, weapply the random matrix theory to the effective Hamiltonian formalism andderive analytically the probability distribution of the complexness parameterfor two statistical ensembles describing the systems invariant under timereversal. For those with rigid spectra, we consider a Hamiltonian characterizedby a picket-fence spectrum without spectral fluctuations. Then, in the morerealistic case of a Hamiltonian described by the Gaussian Orthogonal Ensemble,we reveal and discuss the r\^ole of spectral fluctuations.

Statistics of eigenfunctions in open chaotic systems: a perturbative approach