Generating random numbers by adapted rejection

Random numbers from distributions with densities will be generated in two ways. A ‘stable’ discrete approximation applying Walker’s alias method (a special rejection technique) is used and a version of the rejection method is proposed, which reuses certain random numbers until acceptance is reached. The method relies on reused random numbers which are stochastically independent under specified conditions. The mean number of uniform random numbers, this procedure requires, may be as low as one half compared with the original rejection method.