메뉴 건너뛰기




Volumn 6, Issue , 2001, Pages 1-41

Limit theorems for the number of maxima in random samples from planar regions

Author keywords

Central limit theorems; Convex polygons; Maximal points; Multicriterial optimization; Poisson approximations

Indexed keywords


EID: 0002998733     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v6-76     Document Type: Article
Times cited : (28)

References (39)
  • 1
    • 0033458290 scopus 로고    scopus 로고
    • Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem
    • Aldous, D. and Diaconis, P. (1999). Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem. Bulletin of the American Mathematical Society (New Series) 36 413-432.
    • (1999) Bulletin of the American Mathematical Society (New Series) , vol.36 , pp. 413-432
    • Aldous, D.1    Diaconis, P.2
  • 3
    • 0032222172 scopus 로고    scopus 로고
    • On the variance of the number of maxima in random vectors and its applications
    • Bai, Z.-D., Chao, C.-C., Hwang, H.-K. and Liang, W.-Q. (1998). On the variance of the number of maxima in random vectors and its applications. Annals of Applied Probability 8 886-895.
    • (1998) Annals of Applied Probability , vol.8 , pp. 886-895
    • Bai, Z.-D.1    Chao, C.-C.2    Hwang, H.-K.3    Liang, W.-Q.4
  • 6
    • 0001034387 scopus 로고
    • On the distribution of the number of admissible points in a vector random sample
    • Barndorff-Nielsen, O. and Sobel, M. (1966). On the distribution of the number of admissible points in a vector random sample. Theory of Probability a,n,d its Applications 11 249-269.
    • (1966) Theory of Probability A,N,D Its Applications , vol.11 , pp. 249-269
    • Barndorff-Nielsen, O.1    Sobel, M.2
  • 7
    • 0022786219 scopus 로고
    • The distribution of the number of nondominating variants
    • 24 107-111; translated from Izvestiya Akademii Nauk SSSR. Tekhnicheskaya Kibernetika
    • Baryshnikov, Y. M. (1987) The distribution of the number of nondominating variants. Soviet Journal of Computer and Systems Sciences 24 107-111; translated from Izvestiya Akademii Nauk SSSR. Tekhnicheskaya Kibernetika, 47-50 (1986).
    • (1987) Soviet Journal of Computer and Systems Sciences , pp. 47-50
    • Baryshnikov, Y.M.1
  • 8
    • 0034374793 scopus 로고    scopus 로고
    • Supporting-points processes and some of their applications
    • Baryshnikov, Y. (2000) Supporting-points processes and some of their applications. Probability Theory and Related Fields 117 163-182.
    • (2000) Probability Theory and Related Fields , vol.117 , pp. 163-182
    • Baryshnikov, Y.1
  • 10
    • 0027540720 scopus 로고
    • Fast linear expected-time algorithms for computing maxima and convex hulls
    • Bentley, J. L., Clarkson, L. L. and Levine, D. B. (1993). Fast linear expected-time algorithms for computing maxima and convex hulls. Algorithmica 9 168-183.
    • (1993) Algorithmica , vol.9 , pp. 168-183
    • Bentley, J.L.1    Clarkson, L.L.2    Levine, D.B.3
  • 11
    • 0022440584 scopus 로고
    • Random linear programs with many variables and few constraints
    • Blair, C. (1986). Random linear programs with many variables and few constraints. Mathematical Programming, 34 62-71.
    • (1986) Mathematical Programming , vol.34 , pp. 62-71
    • Blair, C.1
  • 13
    • 0031185117 scopus 로고    scopus 로고
    • Equiaffine inner parallel curves of a plane convex body and the convex hulls of randomly chosen points
    • Buchta, C. and Reitzner, M. (1997). Equiaffine inner parallel curves of a plane convex body and the convex hulls of randomly chosen points. Probability Theory and Related Fields 108 385-415.
    • (1997) Probability Theory and Related Fields , vol.108 , pp. 385-415
    • Buchta, C.1    Reitzner, M.2
  • 14
    • 0003921021 scopus 로고
    • Die Grundlehren der mathematischen Wissenschaften, Band 172, Springer-Verlag, New York
    • Bühlmann, H. (1970). Mathematical Methods in Risk Theory. Die Grundlehren der mathematischen Wissenschaften, Band 172, Springer-Verlag, New York.
    • (1970) Mathematical Methods in Risk Theory
    • Bühlmann, H.1
  • 16
  • 17
    • 85012700045 scopus 로고
    • A note on finding convex hulls via maximal vectors
    • Devroye, L. (1980). A note on finding convex hulls via maximal vectors. Information Processing Letters 11 53-56.
    • (1980) Information Processing Letters , vol.11 , pp. 53-56
    • Devroye, L.1
  • 19
    • 0008411565 scopus 로고
    • Records, the maximal layer, and uniform distributions in monotone sets
    • Devroye, L. (1993). Records, the maximal layer, and uniform distributions in monotone sets. Computers and, Mathematics with Applications 25 19-31.
    • (1993) Computers And, Mathematics with Applications , vol.25 , pp. 19-31
    • Devroye, L.1
  • 20
    • 0041542144 scopus 로고    scopus 로고
    • A note on the expected time for finding maxima by list algorithms
    • Devroye, L. (1999). A note on the expected time for finding maxima by list algorithms. Algorithmica, 23 97-108.
    • (1999) Algorithmica , vol.23 , pp. 97-108
    • Devroye, L.1
  • 21
    • 0012369923 scopus 로고
    • Kindler, gentler, average-case analysis for convex hulls and maximal vectors
    • Dwyer, R. (1990). Kindler, gentler, average-case analysis for convex hulls and maximal vectors. SIGACT News 21 64-71.
    • (1990) SIGACT News , vol.21 , pp. 64-71
    • Dwyer, R.1
  • 23
    • 0029325565 scopus 로고
    • Mellin transforms and asymptotics: Finite differences and Rice’s integrals
    • Flajolet, P. and Sedgewick, R. (1995). Mellin transforms and asymptotics: finite differences and Rice’s integrals. Theoretical Computer Science 144 101-124.
    • (1995) Theoretical Computer Science , vol.144 , pp. 101-124
    • Flajolet, P.1    Sedgewick, R.2
  • 24
    • 21844498465 scopus 로고
    • Probabilistic analysis of an algorithm in the theory of markets in indivisible goods
    • Frieze, A. and Pittel, B. G. (1995). Probabilistic analysis of an algorithm in the theory of markets in indivisible goods. Annals of Applied Probability 5 768-808.
    • (1995) Annals of Applied Probability , vol.5 , pp. 768-808
    • Frieze, A.1    Pittel, B.G.2
  • 26
    • 38249021549 scopus 로고
    • Fast algorithms for direct enclosures and direct dominances
    • Guting, R. H., Nurmi, O. and Ottmann, T. (1989). Fast algorithms for direct enclosures and direct dominances. Journal of Algorithms 10 170-186.
    • (1989) Journal of Algorithms , vol.10 , pp. 170-186
    • Guting, R.H.1    Nurmi, O.2    Ottmann, T.3
  • 28
    • 0032370920 scopus 로고    scopus 로고
    • On convergence rates in the central limit theorems for combinatorial structures
    • Hwang, H.-K. (1998) On convergence rates in the central limit theorems for combinatorial structures. European Journal of Combinatorics 19 329-343.
    • (1998) European Journal of Combinatorics , vol.19 , pp. 329-343
    • Hwang, H.-K.1
  • 29
    • 0033141151 scopus 로고    scopus 로고
    • Asymptotics of Poisson approximation to random discrete distributions: An analytic approach
    • Hwang, H.-K. (1999). Asymptotics of Poisson approximation to random discrete distributions: an analytic approach. Advances in Applied Probability 31 448-491.
    • (1999) Advances in Applied Probability , vol.31 , pp. 448-491
    • Hwang, H.-K.1
  • 34
    • 0039911091 scopus 로고
    • Theorie des elements saillants d’une suite d’observations
    • also in Selected papers of Alfred Renyi, Volume III: 1962-1970, Edited by Pal Turan, Akademiai Kiado, Budapest
    • Renyi, A. (1962). Theorie des elements saillants d’une suite d’observations. Ann. Fac. Sci. Univ. Clermont-Ferrand No. 8, 7-13; also in Selected papers of Alfred Renyi, Volume III: 1962-1970, Edited by Pal Turan, Akademiai Kiado, Budapest (1976).
    • (1962) Ann. Fac. Sci. Univ. Clermont-Ferrand , Issue.8 , pp. 7-13
    • Renyi, A.1
  • 36
    • 0020495641 scopus 로고
    • Survey of estimational results in choice problems
    • Sholomov, L. A. (1984). Survey of estimational results in choice problems. Engineering Cybernetics 21 51-75.
    • (1984) Engineering Cybernetics , vol.21 , pp. 51-75
    • Sholomov, L.A.1
  • 39
    • 0003745767 scopus 로고
    • Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin-New York
    • Zeleny, M. (1974). Linear Multiobjective Programming. Lecture Notes in Economics and Mathematical Systems, Vol. 95, Springer-Verlag, Berlin-New York.
    • (1974) Linear Multiobjective Programming , vol.95
    • Zeleny, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.