Strong consistency of the mean on randomly deleted sets |
| |
| Authors: | Mark D. Rothmann Ralph P. Russo |
| |
| Affiliation: | (1) School of Mathematics, Georgia Institute of Technology, 30332 Atlanta, Georgia;(2) Department of Statistics, University of Iowa, 52242 Iowa City, Iowa |
| |
| Abstract: | Suppose 0 t1<t2<... are fixed points in time. At timetk, a unit with magnitudeXk and lifetimeLk enters a population or is placed into a system. Suppose that theXk's are i.i.d. withEX1= , theLk's are i.i.d., and that theXk's andLk's are independent. In this paper we find conditions under which the continuous time process Avr{Xk:tktk+Lk} is almost surely convergent to . We also demonstrate the sharpness of these conditions. |
| |
| Keywords: | Strong law of large numbers sample means random deletion |
| 本文献已被 SpringerLink 等数据库收录！ |
|
