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Volumn 12, Issue 3, 2006, Pages 501-514

Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality

Author keywords

Compound Poisson process approximation; Coupling inequality; Law of small numbers; Locally dependent variables; Moving sums; Rate of convergence; Success runs; Total variation distance

Indexed keywords


EID: 33846093624     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1151525133     Document Type: Article
Times cited : (3)

References (21)
  • 1
    • 0002005293 scopus 로고
    • Two moments suffice for Poisson approximations: The Chen-Stein method
    • Arratia, R., Goldstein, L. and Gordon, L. (1989) Two moments suffice for Poisson approximations: the Chen-Stein method. Ann. Probab., 17, 9-25.
    • (1989) Ann. Probab. , vol.17 , pp. 9-25
    • Arratia, R.1    Goldstein, L.2    Gordon, L.3
  • 2
    • 84972496740 scopus 로고
    • Poisson approximation and the Chen-Stein method
    • Arratia, R., Goldstein, L. and Gordon, L. (1990) Poisson approximation and the Chen-Stein method. Statist. Sci., 5, 403-434.
    • (1990) Statist. Sci. , vol.5 , pp. 403-434
    • Arratia, R.1    Goldstein, L.2    Gordon, L.3
  • 3
    • 0035413565 scopus 로고    scopus 로고
    • Compound Poisson approximation: A user's guide
    • Barbour A.D. and Chryssaphinou O. (2001) Compound Poisson approximation: a user's guide. Ann. Appl. Probab., 11, 964-1002.
    • (2001) Ann. Appl. Probab. , vol.11 , pp. 964-1002
    • Barbour, A.D.1    Chryssaphinou, O.2
  • 4
    • 0036630899 scopus 로고    scopus 로고
    • Compound Poisson process approximation
    • Barbour, A.D. and Mansson, M. (2002) Compound Poisson process approximation. Ann. Probab., 30, 1492-1537.
    • (2002) Ann. Probab. , vol.30 , pp. 1492-1537
    • Barbour, A.D.1    Mansson, M.2
  • 6
    • 0010486053 scopus 로고    scopus 로고
    • Applications of compound Poisson approximation
    • In Ch. A. Charalambides, M.V. Koutras and N. Balakrishnan (eds), Boca Raton, FL: Chapman & Hall
    • Barbour, A.D., Chryssaphinou, O. and Vaggelatou, E. (2001) Applications of compound Poisson approximation. In Ch. A. Charalambides, M.V. Koutras and N. Balakrishnan (eds), Probability and Statistical Models with Applications, pp. 41-62. Boca Raton, FL: Chapman & Hall.
    • (2001) Probability and Statistical Models With Applications , pp. 41-62
    • Barbour, A.D.1    Chryssaphinou, O.2    Vaggelatou, E.3
  • 7
    • 0034310125 scopus 로고    scopus 로고
    • A bound for the distribution of the sum of discrete associated or negatively associated random variables
    • Boutsikas, M.V. and Koutras, M.V (2000) A bound for the distribution of the sum of discrete associated or negatively associated random variables. Ann. Appl. Probab., 10, 1137-1150.
    • (2000) Ann. Appl. Probab. , vol.10 , pp. 1137-1150
    • Boutsikas, M.V.1    Koutras, M.V.2
  • 8
    • 0008676446 scopus 로고    scopus 로고
    • Compound Poisson approximation for sums of dependent random variables
    • In Ch.A. Charalambides, M.V. Koutras, N. Balakrishnan (eds), Boca Raton, FL: Chapman & Hall
    • Boutsikas, M.V. and Koutras, M.V (2001) Compound Poisson approximation for sums of dependent random variables. In Ch.A. Charalambides, M.V. Koutras, N. Balakrishnan (eds), Probability and Statistical Models with Applications, pp. 63-86. Boca Raton, FL: Chapman & Hall.
    • (2001) Probability and Statistical Models With Applications , pp. 63-86
    • Boutsikas, M.V.1    Koutras, M.V.2
  • 9
  • 10
    • 0036612670 scopus 로고    scopus 로고
    • On the distance between convex-ordered random variables
    • Boutsikas, M.V and Vaggelatou, E. (2002) On the distance between convex-ordered random variables. Adv. Appl. Probab., 34, 349-374.
    • (2002) Adv. Appl. Probab. , vol.34 , pp. 349-374
    • Boutsikas, M.V.1    Vaggelatou, E.2
  • 11
    • 0001067389 scopus 로고
    • Poisson approximation for dependent trials
    • Chen, L.H.Y. (1975). Poisson approximation for dependent trials. Ann. Probab., 3, 534-545.
    • (1975) Ann. Probab. , vol.3 , pp. 534-545
    • Chen, L.H.Y.1
  • 12
    • 4544241299 scopus 로고    scopus 로고
    • Stein's method, Palm theory and Poisson process approximation
    • Chen, L.H.Y. and Xia, A. (2004) Stein's method, Palm theory and Poisson process approximation. Ann. Probab., 32, 2545-2569.
    • (2004) Ann. Probab. , vol.32 , pp. 2545-2569
    • Chen, L.H.Y.1    Xia, A.2
  • 13
    • 0001184792 scopus 로고
    • Poisson approximations for r-scan processes
    • Dembo, A. and Karlin, S. (1992) Poisson approximations for r-scan processes. Ann. Appl. Probab., 2, 329-357.
    • (1992) Ann. Appl. Probab. , vol.2 , pp. 329-357
    • Dembo, A.1    Karlin, S.2
  • 14
    • 0013530368 scopus 로고
    • The Poisson approximation for dependent events
    • Freedmen, D. (1974) The Poisson approximation for dependent events. Ann. Probab., 2, 256-269.
    • (1974) Ann. Probab. , vol.2 , pp. 256-269
    • Freedmen, D.1
  • 15
    • 0032222171 scopus 로고    scopus 로고
    • On the distribution of tail array sums for strongly mixing stationary sequences
    • Rootzén, H., Leadbetter, M.R. and De Haan, L. (1998) On the distribution of tail array sums for strongly mixing stationary sequences. Ann. Appl. Probab., 8, 868-885.
    • (1998) Ann. Appl. Probab. , vol.8 , pp. 868-885
    • Rootzén, H.1    Leadbetter, M.R.2    De Haan, L.3
  • 16
    • 0001443701 scopus 로고
    • A general Poisson approximation theorem
    • Serfling, R.J. (1975) A general Poisson approximation theorem. Ann. Probab., 3, 726-731.
    • (1975) Ann. Probab. , vol.3 , pp. 726-731
    • Serfling, R.J.1
  • 17
    • 0001411184 scopus 로고
    • Some elementary results on Poisson approximations in a sequence of Bernoulli trials
    • Serfling, R.J. (1978) Some elementary results on Poisson approximations in a sequence of Bernoulli trials. SIAM Rev., 20, 567-579.
    • (1978) SIAM Rev. , vol.20 , pp. 567-579
    • Serfling, R.J.1
  • 18
    • 0000087238 scopus 로고
    • Compound Poisson approximation for sums of random variables
    • Serfozo, R. (1986) Compound Poisson approximation for sums of random variables Ann. Probab., 14, 1391-1398.
    • (1986) Ann. Probab. , vol.14 , pp. 1391-1398
    • Serfozo, R.1
  • 19
    • 33748707592 scopus 로고    scopus 로고
    • On compound Poisson approximation for sums of random variables
    • Vellaisamy, P. and Chandburi, B. (1999) On compound Poisson approximation for sums of random variables. Statist. Probab. Lett., 41, 179-189.
    • (1999) Statist. Probab. Lett. , vol.41 , pp. 179-189
    • Vellaisamy, P.1    Chandburi, B.2
  • 20
    • 84988122562 scopus 로고
    • Coupling methods in approximations
    • Wang, Y.H. (1986) Coupling methods in approximations. Canad. J. Statist., 14, 69-74.
    • (1986) Canad. J. Statist. , vol.14 , pp. 69-74
    • Wang, Y.H.1
  • 21
    • 0002542102 scopus 로고
    • From Poisson to compound Poisson approximations
    • Wang, Y.H. (1989) From Poisson to compound Poisson approximations. Math. Sci., 14, 38-49.
    • (1989) Math. Sci. , vol.14 , pp. 38-49
    • Wang, Y.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.