Details
| Original language | English |
|---|---|
| Pages (from-to) | 768-775 |
| Number of pages | 8 |
| Journal | Journal of applied probability |
| Volume | 38 |
| Issue number | 3 |
| Publication status | Published - Sept 2001 |
Abstract
We consider the sum Sd of record values in a sequence of independent random 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 standard renewal theoretic setup. We investigate the distributional limit of Sd and some related quantities as d → ∞. Some explicit values are given for d = 6, a case that can be interpreted as a simple game of chance.
Keywords
- Perpetuities, Records, Uniform distribution
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- General Mathematics
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Journal of applied probability, Vol. 38, No. 3, 09.2001, p. 768-775.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the total time spent in records by a discrete uniform sequence
AU - Grübel, Rudolf
AU - Reimers, Anke
PY - 2001/9
Y1 - 2001/9
N2 - We consider the sum Sd of record values in a sequence of independent random 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 standard renewal theoretic setup. We investigate the distributional limit of Sd and some related quantities as d → ∞. Some explicit values are given for d = 6, a case that can be interpreted as a simple game of chance.
AB - We consider the sum Sd of record values in a sequence of independent random 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 standard renewal theoretic setup. We investigate the distributional limit of Sd and some related quantities as d → ∞. Some explicit values are given for d = 6, a case that can be interpreted as a simple game of chance.
KW - Perpetuities
KW - Records
KW - Uniform distribution
UR - http://www.scopus.com/inward/record.url?scp=0035438324&partnerID=8YFLogxK
U2 - 10.1239/jap/1005091040
DO - 10.1239/jap/1005091040
M3 - Article
AN - SCOPUS:0035438324
VL - 38
SP - 768
EP - 775
JO - Journal of applied probability
JF - Journal of applied probability
SN - 0021-9002
IS - 3
ER -