  We theoretically determine the probability distribution function of the net
field of the random planar structure of dipoles which represent polarized
particles. At small surface concentrations c of the point dipoles this
distribution is expressed in terms of special functions. At the surface
concentrations of the dipoles as high as 0.6 the dipolar field obey the
Gaussian law. To obtain the distribution function within transitional region
c<0.6, we propose the method based on the cumulant expansion. We calculate the
parameters of the distributions for some specific configurations of the
dipoles. The distribution functions of the ordered ensembles of the dipoles at
the low and moderate surface concentrations have asymmetric shape with respect
to distribution medians. The distribution functions allow to calculate various
physical parameters of two-dimensional interacting nanoparticle ensembles.
