The influence of polariton-polariton scattering on the statistics of the polariton condensate in a nonresonantly excited semiconductor microcavity is discussed. Taking advantage of the existence of a bottleneck in the exciton-polariton dispersion curve, the polariton states are separated into two domains: reservoir polaritons inside the bottleneck and active polaritons whose energy lies below the bottleneck. In the framework of the master equation formalism, the nonequilibrium stationary reduced density matrix is calculated and the statistics of polaritons in the condensate at q=0 is determined. The anomalous correlations between the polaritons in the condensate and the active ones are responsible for an enhancement of the noise in the condensate. As a consequence, the second order correlation function of the condensate does not show the full coherence that is characteristic of laser emission.