Sharp Bounds of the Multivariate Discrete Moment Problem: approximations of CDF values and reliability levels

The method of polynomial bases in Mádi-Nagy (2012) can solve almost any type of multivariate discrete moment problem (MDMP) within an acceptable time. The effective implementation of this algorithm is published as a Google hosted project Numerical MDMP (2013), which enables the use of the method in several practical applications. This paper presents three types of applications: approximations of cumulative distribution function (CDF) values of discrete and continuous random vectors and bounding network reliabilities. In case of CDF of discrete random vectors a new bounding method is presented with useful results. For the CDF of continuous random vector our method the most suitable for two-sided bounding among the investigated ones. As regards the network reliability, the new bounds are much better than the other bounds of the comparison. Hence, the polynomial algorithm with its implementation seems to be a useful tool for probability bounding.