English

应用科学学报 ›› 1987, Vol. 5 ›› Issue (4): 301-307.

• 论文 • 上一篇    下一篇

剩余寿命的若干极限性质

糜解   

  1. 上海交通大学
  • 收稿日期:1984-04-03 修回日期:1984-12-04 出版日期:1987-12-31 发布日期:1987-12-31

SOME LIMIT PROPERTIES OF EXCESS LIFE

MI JIE   

  1. Shanghai Jiaotong University
  • Received:1984-04-03 Revised:1984-12-04 Online:1987-12-31 Published:1987-12-31

PDF

74

被引次数

1

摘要： 设非负随机变量T1,T2,…,Tn,…独立同分布,分布函数F为连续,而{N(t),t ≥ 0}是以T1,T2,…为相继到达时间而产生的更新计数过程.本文求出了当t ≥ 0,s ≥ 0时,剩余寿命γ(t)与γ(t+s)的联合分布函数以及其混合矩当t,s→∞时的极限性态.结果表明t,s→∞时,γ(t)和γ(t+s)是渐近独立的.

Abstract: The paper is devoted to the study of excess life in renewal process. It is proved in the paper that the excess life γ(t) and γ(t+s) at time t and t+s respectively are asymptotically independent. And it is also shown that the mixed moment Eγm(t) γn(t+s) equals asymptotically to the product of the limits limt→∞ Eγm(t) and limt→∞ Eγn(s).