Abstract: This paper presents a method for sampling six random variables which indicate three emission angles of gamma rays and three gamma rays energies in the simulation test of three photon annihilation of positrons and electrons From the subsamples produced by the sampling mentioned above, frontier distribution and joint distribution about angles and about energies are obtained. Comparing the present results concerned with the known quantum electrodynamics (QED) prediction and experimental data, it is found that the three results are quite in agreement.