Generating multi-dimensional discrete distribution random number

Multi-dimensional discrete random number plays an important role in computer simulations. However, the existing high-level computer languages usually only give one-dimensional discrete random number, not appease the needs of computer simulation and experiment. Most existing studies focusing on continuous distribution and one-dimensional discrete distribution, in this paper, theory and method on how to obtain random numbers subject to an arbitrary multi-dimensional discrete probability distribution applying random numbers with uniform distribution are given to solve this problem.