Details
| Original language | English |
|---|---|
| Pages (from-to) | 1252-1263 |
| Number of pages | 12 |
| Journal | Annals of Applied Probability |
| Volume | 13 |
| Issue number | 4 |
| Publication status | Published - Nov 2003 |
Abstract
Let Mn be the maximum of a sample X1,...,X n from a discrete distribution and let Wn be the number of i's, 1 ≤ i ≤ n, such that Xi=Mn. We discuss the asymptotic behavior of the distribution of Wn as n → ∞. The probability that the maximum is unique is of interest in diverse problems, for example, in connection with an algorithm for selecting a winner, and has been studied by several authors using mainly analytic tools. We present here an approach based on the Sukhatme-Rényi representation of exponential order statistics, which gives, as we think, a new insight into the problem.
Keywords
- Convergence in distribution, Exponential distribution, Order statistics, Probabilistic constructions, Quantile transformation, Sukhatme-Rényi representation
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Annals of Applied Probability, Vol. 13, No. 4, 11.2003, p. 1252-1263.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the multiplicity of the maximum in a discrete random sample
AU - Bruss, F. Thomas
AU - Grübel, Rudolf
PY - 2003/11
Y1 - 2003/11
N2 - Let Mn be the maximum of a sample X1,...,X n from a discrete distribution and let Wn be the number of i's, 1 ≤ i ≤ n, such that Xi=Mn. We discuss the asymptotic behavior of the distribution of Wn as n → ∞. The probability that the maximum is unique is of interest in diverse problems, for example, in connection with an algorithm for selecting a winner, and has been studied by several authors using mainly analytic tools. We present here an approach based on the Sukhatme-Rényi representation of exponential order statistics, which gives, as we think, a new insight into the problem.
AB - Let Mn be the maximum of a sample X1,...,X n from a discrete distribution and let Wn be the number of i's, 1 ≤ i ≤ n, such that Xi=Mn. We discuss the asymptotic behavior of the distribution of Wn as n → ∞. The probability that the maximum is unique is of interest in diverse problems, for example, in connection with an algorithm for selecting a winner, and has been studied by several authors using mainly analytic tools. We present here an approach based on the Sukhatme-Rényi representation of exponential order statistics, which gives, as we think, a new insight into the problem.
KW - Convergence in distribution
KW - Exponential distribution
KW - Order statistics
KW - Probabilistic constructions
KW - Quantile transformation
KW - Sukhatme-Rényi representation
UR - http://www.scopus.com/inward/record.url?scp=0346913253&partnerID=8YFLogxK
U2 - 10.1214/aoap/1069786498
DO - 10.1214/aoap/1069786498
M3 - Article
AN - SCOPUS:0346913253
VL - 13
SP - 1252
EP - 1263
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 4
ER -