Inequalities for stochastic models via supermodular orderings. (English) Zbl 0871.60015

Bäuerle, Nicole

Commun. Stat., Stochastic Models 13, No. 1, 181-201 (1997).

Summary: The aim of this paper is to derive inequalities for random vectors by using the supermodular ordering. The properties of this ordering suggest to use it as a comparison for the “strength of dependence” in random vectors. In contrast to already established orderings of this type, the supermodular ordering has the advantage that it is not necessary to assume a common marginal distribution for the random vectors under comparison. As a consequence we obtain new inequalities by applying it to multivariate normal distributions, Markov chains and some stochastic models.

MSC:

60E15

Inequalities; stochastic orderings

Keywords:

supermodular ordering; positively dependent random vectors; majorization; Markov chains; multivariate normal distribution; stochastic models