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New method is developed for calculation of single-particle occupation numbers in finite Fermi systems of interacting particles. It is more accurate than the canonical distribution method and gives the Fermi-Dirac distribution in the limit of large number of particles. It is shown that statistical effects of the interaction are absorbed by an increase of the effective temperature. Criteria for quantum chaos and statistical equilibrium are considered. All results are confirmed by numerical experiments in the two-body random interaction model.