Estimation of rare event probabilities by maximum entropy method

Abstract

We propose the use of the maximum entropy method for estimation of rare event probabilities. This method does not presume any distribution function form, but instead flexibly incorporates information from samples as constraints in the associated optimization problem that maximizes the entropy. While the moments information is usually used for MEM, to improve the accuracy of tail probability estimation, we also use tail information from the samples as constraints. We apply this method to several known distributions. We compare our method with the generalized extreme value theory method.