Multivariate new better than used in expectation distributions

Various definitions of multivariate new better than used in expectation (MNBUE) life distributions are introduced and their interrelationships are studied. The definitions are multivariate generalizations of the very useful univariate aging property new better than used in expectations (NBUE), which is weaker than new better than used (NBU) and decreasing mean residual life (DMRL) properties. Various closure properties of the different MNBUE classes are proved. Some examples are given to illustrate the relationship between the proposed MNBUE properties and MNBUE properties presented by Buchanan and Singpurwalla (1977). Examples of well known life distributions, that give rise to the MNBUE distributions are discussed. We also study the dual multivariate new worse than used in expectation (MNWUE) distributions.