Two Basic Partial Orderings for Distributions Derived from Schur Functions and Majorization.

摘要

Researchers in applied fields have long recognized the usefulness of inequalities when exact results are not available. The use of inequalities allows us to say that one estimate is better than another, that one maintenance policy is better than another or that a certain selection procedure is better than another etc., even though, we may not know the best estimator, the best maintenance policy or the best selection procedure. Such results are generally obtained from inequalities between two probability measures or random variables. Inequalities between random variables are in turn obtained from deterministic inequalities or deterministic partial orderings. In this expository paper, the authors describe the essentials of stochastic majorization and DT ordering and demonstrate some applications. A new proof of a slight generalization of earlier results on DT functions is given. (KR)