A study on the cross-entropy method for rare-event probability estimation

We discuss the problem of estimating probabilities of rare events in static simulation models using the recently proposed cross-entropy method, which is a type of importance-sampling technique in which the new distributions are successively calculated by minimizing the cross-entropy with respect to the ideal (but unattainable) zero-variance distribution. In our approach, by working on a functional space we are able to provide an efficient procedure without assuming any specific family of distributions. We then describe an implementable algorithm that incorporates the ideas described in the paper. Some convergence properties of the proposed method are established, and numerical experiments are presented to illustrate the efficacy of the algorithm.