The distinction between coherent and incoherent nonlinear optical interactions is established at the beginning of the paper. In the first part parametric up conversion (PUC) by coherent nonlinear optical mixing of the strong pumping radiation with weak input radiation is treated with respect to statistical properties of generating radiations. The efficiency of PUC is calculated by means of the conserved statistics method. It is shown that the efficiency of PUC depends upon the photon statistics of the strong pumping radiation only, namely, it decreases with increasing fluctuation level in the pumping radiation. The fourth-order statistics of generated sum-frequency radiation is calculated in the first approximation of the iterative solution. The statistics of both generating radiations are projected into the statistical distribution of the resulting sum-frequency radiation in the same way at the beginning of the process.