Abstract
We extend the univariate alpha-quantile residual life function tomultivariate setting preserving its dynamic feature. Principal attributes of this function are derived and their relationship to the dynamic multivariate hazard rate function is discussed. A corresponding ordering, namely, alpha-quantile residual life order, for random vectors of lifetimes is introduced and studied. Based on the proposed ordering, a notion of positive dependency is presented. Finally, a discussion about conditions characterizing the class of decreasing multivariate. alpha-quantile residual life functions is pointed out.