Details
| Original language | English |
|---|---|
| Pages (from-to) | 321-326 |
| Number of pages | 6 |
| Journal | Electronic Notes in Discrete Mathematics |
| Volume | 44 |
| Early online date | 4 Nov 2013 |
| Publication status | Published - 5 Nov 2013 |
Abstract
Let Xi,i∈N, be independent and identically distributed random variables with values in N0. We transform ('prune') the sequence {X1,...,Xn},n∈N, of discrete random samples into a sequence {0,1,2,...,Yn},n∈N, of contiguous random sets by replacing Xn+1 with Yn+1 if Xn+1>Yn. We consider the asymptotic behaviour of Yn as n→∞. Applications include path growth in digital search trees and the number of tables in Pitman's Chinese restaurant process if the latter is conditioned on its limit value.
Keywords
- Chinese restaurant process, Digital search trees, Geometric distribution, Maxima, Tail behaviour
ASJC Scopus subject areas
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Applied Mathematics
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In: Electronic Notes in Discrete Mathematics, Vol. 44, 05.11.2013, p. 321-326.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Pruned discrete random samples
AU - Grübel, Rudolf
AU - Hitczenko, Paweł
PY - 2013/11/5
Y1 - 2013/11/5
N2 - Let Xi,i∈N, be independent and identically distributed random variables with values in N0. We transform ('prune') the sequence {X1,...,Xn},n∈N, of discrete random samples into a sequence {0,1,2,...,Yn},n∈N, of contiguous random sets by replacing Xn+1 with Yn+1 if Xn+1>Yn. We consider the asymptotic behaviour of Yn as n→∞. Applications include path growth in digital search trees and the number of tables in Pitman's Chinese restaurant process if the latter is conditioned on its limit value.
AB - Let Xi,i∈N, be independent and identically distributed random variables with values in N0. We transform ('prune') the sequence {X1,...,Xn},n∈N, of discrete random samples into a sequence {0,1,2,...,Yn},n∈N, of contiguous random sets by replacing Xn+1 with Yn+1 if Xn+1>Yn. We consider the asymptotic behaviour of Yn as n→∞. Applications include path growth in digital search trees and the number of tables in Pitman's Chinese restaurant process if the latter is conditioned on its limit value.
KW - Chinese restaurant process
KW - Digital search trees
KW - Geometric distribution
KW - Maxima
KW - Tail behaviour
UR - http://www.scopus.com/inward/record.url?scp=84887178684&partnerID=8YFLogxK
U2 - 10.1016/j.endm.2013.10.050
DO - 10.1016/j.endm.2013.10.050
M3 - Article
AN - SCOPUS:84887178684
VL - 44
SP - 321
EP - 326
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -