Alternative rare events probability estimation

Estimation of rare event probability is a key issue of recent simulation literature. This topic is of major importance in queuing systems as well as extreme value analysis in many fields such as reliability, telecommunication and insurance risks. However, estimating rare events is a challenging problem from a methodological point of view: since, analytical computation of rare event probabilities can be achieved only for very simple distribution, Monte Carlo approximation have been proposed. In this paper, after a brief review of some recent literature, we propose an alternative method for estimating rare events using simulation: we propose a simple deterministic transform of the random sample drawn from the original distribution such that the rare events become not-so-rare. The new approach can be easily implemented and the resulting estimator can achieve a bounded relative error in some relevant cases such as exponential-like and regularly varying functions. The approach is presented here in a very simple basic setting of a single random variable but it can be also extended to sum of random variables