Accuracy in random number generation

The generation of continuous random variables on a digital computer encounters a problem of accuracy caused by approximations and discretization error. These in turn impose a bias on the simulation results. An ideal discrete approximation of a continuous distribution and a measure of error are proposed. Heuristic analysis of common methods for transforming uniform deviates to other continuous random variables is discussed. Comments and recom- mendations are made for the design of algorithms to reduce the bias and avoid overflow problems.