摘要
本文讨论了两类寿命分布与指数分布之间的贴近性.记 F 是均值为1,二阶矩为μ2的寿命分布,F=1-F,.主要结果为:(1)若 F∈DMRL,记 p=1-(μ2)/2,则a)b)c)(2)若 F∈HNWUE,,且μ2<<∞。,则进一步此上界还可改善为(13)。最后,还讨论了(t)-e^(-e)的界.
In this paper we discuss the proximity of two classes of life distributions to the exp- onential distributions.Let F be a life distribution with mean 1,and denote μ2 is the second moment of F,(t)=integral from t to 8 (u)du,=1-F.The maim results are.(1) If f ∈ DMRL,thena) |(t)-e^(-t)|≤1-e^(-2p),b)0≤e^(-t)-(t)≤p,c) 0≤(t)-(t)≤ 2p,where ρ=1-μ2/2.(2) If F ∈HNWUE,and μ2 is finite,then |(t)-e^(-t)|≤ (36ρ/(3+2ρ^(1/2)~2)^(1/3) where ρ=μ2/2-1.In addition,the upper bound can be improved as (6).Finally,we disouss the bound of (t)-e^(-t).
出处
《应用概率统计》
CSCD
北大核心
1989年第1期45-53,共9页
Chinese Journal of Applied Probability and Statistics
基金
国家自然科学基金
