For the first time applications of probability densities constructed on the atomic functions (AF) theory for analysis and synthesis for linear arrays are considered. Average characteristics of linear arrays with random phase errors are studied such as average directional diagram (DD), average directive gain (DG), beam width (BW), and side lobe level. Introduced errors correlation coefficient based on AF and the law of errors distribution is Kravchenko-Rvachov distribution. Correlation field characteristics are constructed for the cases when the probability densities of envelopes DD are Kravchenko-Rayleigh and Kravchenko-Gauss distributions. In this case a far-field boundary of antenna with random errors in gain-phase source distributions is defined. Thus a far-field is defined for two characteristics of antennas which are average DD and correlation fluctuations function of complex field an executed numerical experiment for the Gaussian and Kravchenko-Rvachov distribution as well as Kravchenko-Gauss has shown efficiency of introduced approach.