Statistical characteristics of radiation intensity in the cross section of laser beams propagating in the turbulent atmosphere are analyzed by using numerical simulations. It is shown that for arbitrary values of the propagation distance, Rytov parameter, beam type, and position of the analyzed point in the beam cross section, the probability density function (PDF) of radiation intensity is fully determined by the scintillation index and the average intensity. In the case of moderate and weak intensity fluctuations characterized by the scintillation index smaller than unity, the probability density function is determined by the gamma distribution. For the case of strong fluctuations (with the scintillation index larger than unity), a new analytical expression for PDF is proposed, which well approximates PDFs obtained in numerical experiments under different conditions of propagation of different-type beams.