  We study the statistics of the gravitational (Newtonian) force in a
particular kind of weakly correlated distribution of point-like and unitary
mass particles generated by the so-called Gauss-Poisson point process. In
particular we extend to these distributions the analysis a' la Chandrasekhar
introduced for purely Poisson processes. In this way we can find the asymptotic
behavior of the probability density function of the force for large values of
the field as a generalization of the Holtzmark statistics. The validity of the
introduced approximations is positively tested through a direct comparison with
the analysis of the statistics of the gravitational force in numerical
simulations of Gauss-Poisson processes. Moreover the statistics of the force
felt by a particle due to only its first nearest neighbor is analytically a
numerical studied, resulting to be the dominant contribution to the total
force.
