CONCEPTS OF DEPENDENCE AND STOCHASTIC ORDER FOR BIVARIANTE PROBABILITY-DISTRIBUTION

Yanagimoto and Okamoto (1969) introduced a stochastic ordering that generalizes a concept of monotone regression dependence introduced by Lehmann (1966). In this paper, we define and examine the properties of three new orderings which imply that of Yanagimoto and Okamoto. One of these orderings is seen to extend Shaked's (1977) notion of DTP(0,1), and another includes Lehmann's concept of positive likelihood-ratio dependence as a special case. The proposed orderings are also compared with the TP2 positive-dependence ordering defined by Kimeldorf and Sampson (1987).