BOUNDING THE STOCHASTIC PERFORMANCE OF CONTINUUM STRUCTURE FUNCTIONS. I

Abstract : A continuum structure function gamma is a nondecreasing mapping from the unit hypercube to the unit interval. Minimal path (cut) sets of upper (lower) simple continuum structure functions are introduced and are used to determine bounds on the distribution of gamma (X) when X is a vector of associated random variables and when is right (left)-continuous. It is shown that, if gamma admits of a modular decomposition, improved bounds may be obtained. (Author)