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 in...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 B<sub>2</sub>=（?）,α=1-（B<sub>2</sub>）/（μ<sup>2</sup>）,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<sup>-2α</sup>).2)If X∈（D） NBUE （discrete new better than use in expectation） thenΔ（X,Y）≤max(α,1-e<sup>-（2α）<sup>1/2</sup></sup>.展开更多
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 ...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.展开更多
基金Supported by the NNSF of China(Grant No.:10171093)the National 973 Fundamental Research Program on Financial Engineering(Grant No:G1998030418)the Doctoral Program Foundation of Institute of High Education.
基金This project was supported by grant No.1880492 from the National Natural Science Foundation of China
文摘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 B<sub>2</sub>=（?）,α=1-（B<sub>2</sub>）/（μ<sup>2</sup>）,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<sup>-2α</sup>).2)If X∈（D） NBUE （discrete new better than use in expectation） thenΔ（X,Y）≤max(α,1-e<sup>-（2α）<sup>1/2</sup></sup>.
文摘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.
