Two classes of multivariate DMRL distributions and a class of multivariate NBUE distributions are introduced in this paper by using conditional stochastic order.That is, a random vector belongs to a multivariate DMRL class of life distributions if its residual life(defined as a conditional random vector)is decreasing in time under convex or linear order.Some conservation properties of these classes are studied.
In this paper we discuss the problem of approximating distributions in certain discretelife classes.Let X be a random variable（r.v.）taking nonnegative integers,EX=μ.Suppose Yis a geometric r.v.taking nonnegative integers and with the same mean μ.Denote B2=（?）,α=1-（B2）/（μ2）,Δ（X,Y）=（?）|P（X≥k）-P（Y≥k）|.The main results are:1)If X∈（D） DMRL （discrete decreasing mean residual life）,thenΔ（X,Y）≤max(α,1-e-2α).2)If X∈（D） NBUE （discrete new better than use in expectation） thenΔ（X,Y）≤max(α,1-e-（2α）1/2.
