On the total time spent in records by a discrete uniform sequence

Authors
Grubel, R Reimers, A
Citation
R. Grubel et A. Reimers, On the total time spent in records by a discrete uniform sequence, J APPL PROB, 38(3), 2001, pp. 768-775
Citations number
11
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF APPLIED PROBABILITY
ISSN journal
00219002 → ACNP
Volume
38
Issue
3
Year of publication
2001
Pages
768 - 775
Database
ISI
SICI code
0021-9002(200109)38:3<768:OTTTSI>2.0.ZU;2-7
Abstract
We consider the sum S-d of record values in a sequence of independent rando m variables that are uniformly distributed on 1, . . . , d. This sum can be interpreted as the total amount of time spent in record lifetimes in the s tandard renewal theoretic setup. We investigate the distributional limit of S-d and some related quantities as d --> infinity. Some explicit values ar e given for d = 6, a case that can be interpreted as a simple game of chanc e.