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Volumn 32, Issue 1, 2000, Pages 19-38

Compound poisson approximation and the clustering of random points

Author keywords

Compound Poisson approximation; Stein's method

Indexed keywords


EID: 0002754840     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800009745     Document Type: Article
Times cited : (6)

References (20)
  • 2
    • 0003099908 scopus 로고    scopus 로고
    • On the distribution of scan statistics of a two-dimensional Poisson process
    • ALM, S. E. (1997). On the distribution of scan statistics of a two-dimensional Poisson process. Adv. Appl. Prob. 29, 1-18.
    • (1997) Adv. Appl. Prob. , vol.29 , pp. 1-18
    • Alm, S.E.1
  • 3
    • 0038870266 scopus 로고    scopus 로고
    • Stein's method
    • Update, eds S. Kotz, C. B. Read and D. L. Banks. John Wiley. New York
    • BARBOUR, A. D. (1997). Stein's method. In Encyclopaedia of Statistical Sciences, Update, Vol. 1, eds S. Kotz, C. B. Read and D. L. Banks. John Wiley. New York, pp. 513-521.
    • (1997) Encyclopaedia of Statistical Sciences , vol.1 , pp. 513-521
    • Barbour, A.D.1
  • 5
    • 0001837365 scopus 로고    scopus 로고
    • Compound Poisson approximation in total variation
    • BARBOUR, A. D. AND UTEV, S. (1999). Compound Poisson approximation in total variation. Stoch. Proc. Appl. 82, 89-125.
    • (1999) Stoch. Proc. Appl. , vol.82 , pp. 89-125
    • Barbour, A.D.1    Utev, S.2
  • 6
    • 0000549988 scopus 로고
    • Compound Poisson approximation for non-negative random variables via Stein's method
    • BARBOUR, A. D., CHEN, L. H. Y. AND LOH, W.-L. (1992a). Compound Poisson approximation for non-negative random variables via Stein's method. Ann. Prob. 20, 1843-1866.
    • (1992) Ann. Prob. , vol.20 , pp. 1843-1866
    • Barbour, A.D.1    Chen, L.H.Y.2    Loh, W.-L.3
  • 8
    • 0039079138 scopus 로고
    • A problem in the random distribution of particles
    • EGGLETON, P. AND KERMACK, W. O. (1944). A problem in the random distribution of particles. Proc. Roy. Soc. Edinb. Sect. A 62, 103-115.
    • (1944) Proc. Roy. Soc. Edinb. Sect. A , vol.62 , pp. 103-115
    • Eggleton, P.1    Kermack, W.O.2
  • 9
    • 84990712091 scopus 로고
    • Poisson approximation for large deviations
    • JANSON, S. (1990). Poisson approximation for large deviations. Random Structures Algorithms 1, 221-230.
    • (1990) Random Structures Algorithms , vol.1 , pp. 221-230
    • Janson, S.1
  • 10
    • 0000252769 scopus 로고
    • Large-deviation approximations to the distribution of scan statistics
    • LOADER, C. R. (1991). Large-deviation approximations to the distribution of scan statistics. Adv. Appl. Prob. 23, 751-771.
    • (1991) Adv. Appl. Prob. , vol.23 , pp. 751-771
    • Loader, C.R.1
  • 11
    • 0040857504 scopus 로고
    • k(n), the probable number of k-aggregates in a random distribution of n points
    • k(n), the probable number of k-aggregates in a random distribution of n points. Phil. Mag. 39, 778-790.
    • (1948) Phil. Mag. , vol.39 , pp. 778-790
    • Mack, C.1
  • 12
    • 84959695857 scopus 로고
    • The expected number of aggregates in a random distribution of n points
    • MACK, C. (1949). The expected number of aggregates in a random distribution of n points. Proc. Cambridge Phil. Soc. 46, 285-292.
    • (1949) Proc. Cambridge Phil. Soc. , vol.46 , pp. 285-292
    • Mack, C.1
  • 13
    • 0040843329 scopus 로고    scopus 로고
    • Poisson approximation in connection with clustering of random points
    • MÅNSSON, M. (1999a). Poisson approximation in connection with clustering of random points. Ann. Appl. Prob. 9, 465-492.
    • (1999) Ann. Appl. Prob. , vol.9 , pp. 465-492
    • Månsson, M.1
  • 14
    • 0004250397 scopus 로고    scopus 로고
    • On Poisson approximation for continuous multiple scan statistics in two dimensions
    • eds J. Glaz and N. Balakrishnan. Birkhäuser, Boston
    • MÅNSSON, M. (1999b). On Poisson approximation for continuous multiple scan statistics in two dimensions. In Scan Statistics and Applications, eds J. Glaz and N. Balakrishnan. Birkhäuser, Boston, pp. 225-297.
    • (1999) Scan Statistics and Applications , pp. 225-297
    • Månsson, M.1
  • 15
    • 0011568576 scopus 로고
    • Compound Poisson approximations for the numbers of extreme spacings
    • ROOS, M. (1993). Compound Poisson approximations for the numbers of extreme spacings. Adv. Appl. Prob. 25, 847-874.
    • (1993) Adv. Appl. Prob. , vol.25 , pp. 847-874
    • Roos, M.1
  • 16
    • 0000816829 scopus 로고
    • Stein's method for compound Poisson approximation: The local approach
    • ROOS, M. (1994a). Stein's method for compound Poisson approximation: the local approach. Ann. Appl. Prob. 4, 1177-1187.
    • (1994) Ann. Appl. Prob. , vol.4 , pp. 1177-1187
    • Roos, M.1
  • 17
    • 0002321617 scopus 로고
    • Stein-Chen method for compound Poisson approximation: The coupling approach
    • ed. B. Gigelionis et al. TEV, Vilnius
    • ROOS, M. (1994b). Stein-Chen method for compound Poisson approximation: the coupling approach. In Probability Theory and Mathematical Statistics. Proc. Sixth Vilnius Conf., ed. B. Gigelionis et al. TEV, Vilnius, pp. 645-660.
    • (1994) Probability Theory and Mathematical Statistics. Proc. Sixth Vilnius Conf. , pp. 645-660
    • Roos, M.1
  • 18
    • 0039671386 scopus 로고
    • The probable number of aggregates in random distributions of points
    • SILBERSTEIN, L. (1945). The probable number of aggregates in random distributions of points. Phil. Mag. 36, 319-336.
    • (1945) Phil. Mag. , vol.36 , pp. 319-336
    • Silberstein, L.1
  • 19
    • 0001611740 scopus 로고
    • Short distances, flat triangles and Poisson limits
    • SILVERMAN, B. W. AND BROWN, T. C. (1978). Short distances, flat triangles and Poisson limits. J. Appl. Prob. 15, 815-825.
    • (1978) J. Appl. Prob. , vol.15 , pp. 815-825
    • Silverman, B.W.1    Brown, T.C.2
  • 20
    • 0002310037 scopus 로고
    • Rates of Poisson convergence for U-statistics
    • SILVERMAN, B. W. AND BROWN, T. C. (1979). Rates of Poisson convergence for U-statistics. J. Appl. Prob. 16, 428-432.
    • (1979) J. Appl. Prob. , vol.16 , pp. 428-432
    • Silverman, B.W.1    Brown, T.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.