메뉴 건너뛰기




Volumn 11, Issue 3, 2001, Pages 964-1002

Compound poisson approximation: A user's guide

Author keywords

Compound poisson; Kolmogorov distance; Stein's method; Total variation distance

Indexed keywords


EID: 0035413565     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1015345355     Document Type: Article
Times cited : (70)

References (63)
  • 2
    • 0002005293 scopus 로고
    • Two moments suffice for poisson approximation: The Chen-Stein method
    • ARRATIA, R., GOLDSTEIN, L. and GORDON, L. (1989). Two moments suffice for Poisson approximation: 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
  • 3
    • 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. 5 403-34.
    • (1990) Statist. Sci. , vol.5 , pp. 403-434
    • Arratia, R.1    Goldstein, L.2    Gordon, L.3
  • 4
    • 0000960430 scopus 로고
    • The Erdos-Rényi law in distribution, for coin tossing and sequence matching
    • ARRATIA, R., GORDON, L. and WATERMAN, M. S. (1990). The Erdos-Rényi law in distribution, for coin tossing and sequence matching. Ann. Statist. 18 539-570.
    • (1990) Ann. Statist. , vol.18 , pp. 539-570
    • Arratia, R.1    Gordon, L.2    Waterman, M.S.3
  • 5
    • 0029792949 scopus 로고    scopus 로고
    • Poisson process approximation for sequence repeats and sequencing by hybridization
    • ARRATIA, R., MARTIN, D., REINERT, G. and WATERMAN, M. S. (1996). Poisson process approximation for sequence repeats and sequencing by hybridization. J. Comp. Biol. 3 425-463.
    • (1996) J. Comp. Biol. , vol.3 , pp. 425-463
    • Arratia, R.1    Martin, D.2    Reinert, G.3    Waterman, M.S.4
  • 6
    • 0007212459 scopus 로고    scopus 로고
    • Topics in poisson approximation
    • To appear
    • BARBOUR, A. D. (1999). Topics in Poisson approximation. Handbook of Statistics. To appear.
    • (1999) Handbook of Statistics
    • Barbour, A.D.1
  • 7
    • 0000549988 scopus 로고
    • Compound poisson approximation for nonnegative random variables via Stein's method
    • BARBOUR, A. D., CHEN, L. H. Y. and LOH, W.-L. (1992). Compound Poisson approximation for nonnegative random variables via Stein's method. Ann. Probab. 20 1843-1866.
    • (1992) Ann. Probab. , vol.20 , pp. 1843-1866
    • Barbour, A.D.1    Chen, L.H.Y.2    Loh, W.-L.3
  • 9
    • 0030105250 scopus 로고    scopus 로고
    • Compound poisson approximation in systems reliability
    • BARBOUR, A. D., CHRYSSAPHINOU, O. and ROOS, M. (1996). Compound Poisson approximation in systems reliability. Naval Res. Logist. 43 251-264.
    • (1996) Naval Res. Logist. , vol.43 , pp. 251-264
    • Barbour, A.D.1    Chryssaphinou, O.2    Roos, M.3
  • 10
    • 0010486053 scopus 로고    scopus 로고
    • Applications of compound poisson approximation
    • (N. Balakrishnan, M. V. Koutras and C. Charalambides, eds.) CRC Press, Boca Raton, FL
    • BARBOUR, A. D., CHRYSSAPHINOU, O. and VAGGELATOU, E. (2000). Applications of compound Poisson approximation. In Statistical Distribution Theory and Inference (N. Balakrishnan, M. V. Koutras and C. Charalambides, eds.) CRC Press, Boca Raton, FL.
    • (2000) Statistical Distribution Theory and Inference
    • Barbour, A.D.1    Chryssaphinou, O.2    Vaggelatou, E.3
  • 13
    • 0002754840 scopus 로고    scopus 로고
    • Compound poisson approximation and the clustering of random points
    • BARBOUR, A. D. and MÅNSSON, M. (2000). Compound Poisson approximation and the clustering of random points. Adv. in Appl. Probab. 32 19-38.
    • (2000) Adv. in Appl. Probab. , vol.32 , pp. 19-38
    • Barbour, A.D.1    Månsson, M.2
  • 14
    • 0000150105 scopus 로고    scopus 로고
    • Solving the Stein equation in compound poisson approximation
    • BARBOUR, A. D. and UTEV, S. (1998). Solving the Stein equation in compound Poisson approximation. Adv. in Appl. Probab. 30 449-475.
    • (1998) Adv. in Appl. Probab. , vol.30 , pp. 449-475
    • Barbour, A.D.1    Utev, S.2
  • 15
    • 0001837365 scopus 로고    scopus 로고
    • Compound poisson approximation in total variation
    • BARBOUR, A. D. and UTEV, S. (1999). Compound Poisson approximation in total variation. Stochastic Process. Appl. 82 89-125.
    • (1999) Stochastic Process. Appl. , vol.82 , pp. 89-125
    • Barbour, A.D.1    Utev, S.2
  • 16
    • 0000220023 scopus 로고    scopus 로고
    • Estimating Stein's constants for compound poisson approximation
    • BARBOUR, A. D. and XIA, A. (2000). Estimating Stein's constants for compound Poisson approximation. Bernoulli. 6 581-590.
    • (2000) Bernoulli , vol.6 , pp. 581-590
    • Barbour, A.D.1    Xia, A.2
  • 17
    • 84996136249 scopus 로고    scopus 로고
    • Poisson perturbations
    • BARBOUR, A. D. and XIA, A. (1999). Poisson perturbations. ESAIM: P&S 3 131-150.
    • (1999) ESAIM: P&S , vol.3 , pp. 131-150
    • Barbour, A.D.1    Xia, A.2
  • 18
    • 0000793661 scopus 로고
    • Optimum redundancy when components are subject to two kinds of failure
    • BARLOW, R. E., HUNTER, L. C. and PROSCHAN, F. (1963). Optimum redundancy when components are subject to two kinds of failure. J. Soc. Indust. Appl. Math. 11 64-73.
    • (1963) J. Soc. Indust. Appl. Math. , vol.11 , pp. 64-73
    • Barlow, R.E.1    Hunter, L.C.2    Proschan, F.3
  • 19
    • 0029274603 scopus 로고
    • A survey of the reliability studies of consecutive-k-out-of-n:F system and related systems
    • CHAO, M. T., FU, J. C. and KOUTRAS, M. V. (1995). A survey of the reliability studies of consecutive-k-out-of-n:F system and related systems. IEEE Trans. Reliability 44 120-127.
    • (1995) IEEE Trans. Reliability , vol.44 , pp. 120-127
    • Chao, M.T.1    Fu, J.C.2    Koutras, M.V.3
  • 20
    • 0030527253 scopus 로고    scopus 로고
    • Two-dimensional discrete scan statistics
    • CHEN, J. and GLAZ, J. (1996). Two-dimensional discrete scan statistics. Statist. Probab. Let. 31 59-68.
    • (1996) Statist. Probab. Let. , vol.31 , pp. 59-68
    • Chen, J.1    Glaz, J.2
  • 21
    • 0027668411 scopus 로고
    • Consecutive-2-out-of-n-:F systems with node and link failures
    • CHEN, R. W., HWANG, F. K. and LI, W.-C. W. (1993). Consecutive-2-out-of-n-:F systems with node and link failures. IEEE Trans. Reliability 42 497-502.
    • (1993) IEEE Trans. Reliability , vol.42 , pp. 497-502
    • Chen, R.W.1    Hwang, F.K.2    Li, W.-C.W.3
  • 22
    • 0001766090 scopus 로고
    • A limit theorem for the number of overlapping appearances of a pattern in a sequence of independent trials
    • CHRYSSAPHINOU, O. and PAPASTAVRIDIS, S. (1988). A limit theorem for the number of overlapping appearances of a pattern in a sequence of independent trials. Probab. Theory Related Fields 79 129-143.
    • (1988) Probab. Theory Related Fields , vol.79 , pp. 129-143
    • Chryssaphinou, O.1    Papastavridis, S.2
  • 23
    • 0007206525 scopus 로고
    • Limit distribution for a consecutive-k-out-of-n:F system
    • CHRYSSAPHINOU, O. and PAPASTAVRIDIS, S. (1990). Limit distribution for a consecutive-k-out-of-n:F system. Adv. in Appl. Probab. 22 491-493.
    • (1990) Adv. in Appl. Probab. , vol.22 , pp. 491-493
    • Chryssaphinou, O.1    Papastavridis, S.2
  • 25
    • 0007212461 scopus 로고    scopus 로고
    • Poisson approximation for the nonoverlapping appearances of several words in Markov chains
    • To appear
    • CHRYSSAPHINOU, O., PAPASTAVRIDIS, S. AND VAGGELATOU, E. (2000). Poisson approximation for the nonoverlapping appearances of several words in Markov chains. Combin. Probab. Comput. To appear.
    • (2000) Combin. Probab. Comput.
    • Chryssaphinou, O.1    Papastavridis, S.2    Vaggelatou, E.3
  • 26
    • 0007265314 scopus 로고    scopus 로고
    • Compound poisson approximation for the numbers of long increasing sequences
    • To appear
    • CHRYSSAPHINOU, O. and VAGGELATOU, E. (1999a). Compound Poisson approximation for the numbers of long increasing sequences. J. Appl. Probab. To appear.
    • (1999) J. Appl. Probab.
    • Chryssaphinou, O.1    Vaggelatou, E.2
  • 27
    • 0007211384 scopus 로고    scopus 로고
    • Compound poisson approximation for multiple runs in a Markov chain
    • To appear
    • CHRYSSAPHINOU, O. and VAGGELATOU, E. (1999b). Compound Poisson approximation for multiple runs in a Markov chain. Ann. Inst. Statist. Math. To appear.
    • (1999) Ann. Inst. Statist. Math.
    • Chryssaphinou, O.1    Vaggelatou, E.2
  • 28
    • 0033432266 scopus 로고    scopus 로고
    • Compound poisson approximation for dissociated random variables via Stein's method
    • EICHELSBACHER, P. and ROOS, M. (1999). Compound Poisson approximation for dissociated random variables via Stein's method. Combin. Probab. Computing 8 335-346.
    • (1999) Combin. Probab. Computing , vol.8 , pp. 335-346
    • Eichelsbacher, P.1    Roos, M.2
  • 29
    • 0007341024 scopus 로고
    • Oxford Univ. Press
    • ENGLE, R. (1995). ARCH. Oxford Univ. Press.
    • (1995) ARCH
    • Engle, R.1
  • 31
    • 0033244644 scopus 로고    scopus 로고
    • Compound poisson approximation for Markov chains using Stein's method
    • ERHARDSSON, T. (1999). Compound Poisson approximation for Markov chains using Stein's method. Ann. Appl. Probab. 27 565-596.
    • (1999) Ann. Appl. Probab. , vol.27 , pp. 565-596
    • Erhardsson, T.1
  • 32
    • 0000435984 scopus 로고
    • Poisson approximations for two-dimensional patterns
    • FU, J. C. and KOUTRAS, M. V. (1994). Poisson approximations for two-dimensional patterns. Ann. Inst. Statist. Math. 46 179-192.
    • (1994) Ann. Inst. Statist. Math. , vol.46 , pp. 179-192
    • Fu, J.C.1    Koutras, M.V.2
  • 34
    • 0029728655 scopus 로고    scopus 로고
    • Discrete scan statistics with applications to minefield detection
    • GLAZ, J. (1996). Discrete scan statistics with applications to minefield detection. In SPIE 2765 420-429.
    • (1996) SPIE , vol.2765 , pp. 420-429
    • Glaz, J.1
  • 36
    • 0041805921 scopus 로고
    • Poisson approximations for the distribution and moments of ordered m-spacings
    • GLAZ, J., NAUS, J., ROOS, M. and WALLENSTEIN, S. (1994). Poisson approximations for the distribution and moments of ordered m-spacings. J. Appl. Probab. 31 271-281.
    • (1994) J. Appl. Probab. , vol.31 , pp. 271-281
    • Glaz, J.1    Naus, J.2    Roos, M.3    Wallenstein, S.4
  • 37
    • 0000309739 scopus 로고
    • Poisson approximations for runs and patterns of rare events
    • GODBOLE, A. (1991). Poisson approximations for runs and patterns of rare events. Adv. in Appl. Probab. 23 851-865.
    • (1991) Adv. in Appl. Probab. , vol.23 , pp. 851-865
    • Godbole, A.1
  • 38
    • 0002845889 scopus 로고
    • Improved poisson approximations for word patterns
    • GODBOLE, A. P. and SCHAFFNER, A. A. (1993). Improved Poisson approximations for word patterns. Adv. in Appl. Probab. 25 334-347.
    • (1993) Adv. in Appl. Probab. , vol.25 , pp. 334-347
    • Godbole, A.P.1    Schaffner, A.A.2
  • 39
    • 0030137191 scopus 로고    scopus 로고
    • The compound poisson approximation for a portfolio of dependent risks
    • GOOVAERTS, M. J. and DHAENE, J. (1996). The compound Poisson approximation for a portfolio of dependent risks. Insurance Math. Econom. 18 81-85.
    • (1996) Insurance Math. Econom. , vol.18 , pp. 81-85
    • Goovaerts, M.J.1    Dhaene, J.2
  • 40
    • 0031324697 scopus 로고    scopus 로고
    • Approximating the distribution of the scan statistic using moments of the number of clumps
    • HUFFER, F. and LIN, C. T. (1997). Approximating the distribution of the scan statistic using moments of the number of clumps. J. Amer. Statist. Soc. 92 1466-1475.
    • (1997) J. Amer. Statist. Soc. , vol.92 , pp. 1466-1475
    • Huffer, F.1    Lin, C.T.2
  • 41
    • 84990712091 scopus 로고
    • Poisson approximation for large deviations
    • JANSON, S. (1990). Poisson approximation for large deviations. Random Structures Algorithms 1 221-229.
    • (1990) Random Structures Algorithms , vol.1 , pp. 221-229
    • Janson, S.1
  • 42
    • 0032221888 scopus 로고    scopus 로고
    • New versions of Suen's correlation inequality
    • JANSON, S. (1998). New versions of Suen's correlation inequality. Random Structures Algorithms 13 467-483.
    • (1998) Random Structures Algorithms , vol.13 , pp. 467-483
    • Janson, S.1
  • 43
    • 0031126493 scopus 로고    scopus 로고
    • Consecutive-k, r-out-of-n:DFM systems
    • KOUTRAS, M. V. (1997). Consecutive-k, r-out-of-n:DFM systems. Microelectron. Reliab. 37 597-603.
    • (1997) Microelectron. Reliab. , vol.37 , pp. 597-603
    • Koutras, M.V.1
  • 45
    • 0001043914 scopus 로고
    • An approximation theorem for the poisson binomial distribution
    • LE CAM, L. (1960). An approximation theorem for the Poisson binomial distribution. Pacific J. Math. 10 1181-1197.
    • (1960) Pacific J. Math. , vol.10 , pp. 1181-1197
    • Le Cam, L.1
  • 47
    • 84974488996 scopus 로고
    • An improved error bound for the compound poisson approximation of a nearly homogeneous portfolio
    • MICHEL, R. (1988). An improved error bound for the compound Poisson approximation of a nearly homogeneous portfolio. ASTIN Bulletin 17 165-169.
    • (1988) ASTIN Bulletin , vol.17 , pp. 165-169
    • Michel, R.1
  • 48
    • 21844500006 scopus 로고
    • A poisson approximation for sequence comparisons with insertions and deletions
    • NEUHAUSER, C. (1994). A Poisson approximation for sequence comparisons with insertions and deletions. Ann. Statist. 22 1603-1629.
    • (1994) Ann. Statist. , vol.22 , pp. 1603-1629
    • Neuhauser, C.1
  • 49
    • 17644389210 scopus 로고    scopus 로고
    • A phase transition for the distribution of matching blocks
    • NEUHAUSER, C. (1996). A phase transition for the distribution of matching blocks. Combin. Probab. Comput. 5 139-159.
    • (1996) Combin. Probab. Comput. , vol.5 , pp. 139-159
    • Neuhauser, C.1
  • 50
    • 0000774604 scopus 로고
    • Limiting behavior of a process of runs
    • PITTEL, B. G. (1981). Limiting behavior of a process of runs. Ann. Probab. 9 119-129.
    • (1981) Ann. Probab. , vol.9 , pp. 119-129
    • Pittel, B.G.1
  • 51
    • 0000622770 scopus 로고
    • Generalized Gibbs states and Markov random fields
    • PRESTON, C. J. (1973). Generalized Gibbs states and Markov random fields. Adv. in Appl. Probab. 5 242-261.
    • (1973) Adv. in Appl. Probab. , vol.5 , pp. 242-261
    • Preston, C.J.1
  • 52
    • 0031902984 scopus 로고    scopus 로고
    • Compound poisson and poisson process approximations for occurrences of multiple words in Markov chains
    • REINERT, G., and SCHBATH, S. (1998). Compound Poisson and Poisson process approximations for occurrences of multiple words in Markov chains. J. Comp. Biol. 5 223-253.
    • (1998) J. Comp. Biol. , vol.5 , pp. 223-253
    • Reinert, G.1    Schbath, S.2
  • 53
    • 0001385035 scopus 로고
    • Three problems on the lengths of increasing runs
    • RÉVÉSZ, P. (1983). Three problems on the lengths of increasing runs. Stochastic Process. Appl. 15 169-179.
    • (1983) Stochastic Process. Appl. , vol.15 , pp. 169-179
    • Révész, P.1
  • 55
    • 0000816829 scopus 로고
    • Stein's method for compound poisson approximation: The local approach
    • ROOS, M. (1994). Stein's method for compound Poisson approximation: the local approach. Ann. Appl. Probab. 4 1177-1187.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 1177-1187
    • Roos, M.1
  • 56
    • 0000406309 scopus 로고
    • Multivalued state component systems
    • ROSS, S. (1979). Multivalued state component systems. Ann. Probab. 7 379-383.
    • (1979) Ann. Probab. , vol.7 , pp. 379-383
    • Ross, S.1
  • 57
    • 0025472655 scopus 로고
    • Two-dimensional consecutive-k-out-of-n:F models
    • SALVIA, A. A., and LASHER, W. C. (1990). Two-dimensional consecutive-k-out-of-n:F models. IEEE Trans. Reliability 39 382-385.
    • (1990) IEEE Trans. Reliability , vol.39 , pp. 382-385
    • Salvia, A.A.1    Lasher, W.C.2
  • 59
    • 84996141000 scopus 로고
    • Compound poisson approximation of word counts in DNA sequences
    • SCHBATH, S. (1995). Compound Poisson approximation of word counts in DNA sequences. ESAIM: P&S 1 1-16.
    • (1995) ESAIM: P&S , vol.1 , pp. 1-16
    • Schbath, S.1
  • 60
    • 84990652711 scopus 로고
    • A correlation inequality and a poisson limit theorem for nonoverlapping balanced subgraphs of a random graph
    • SUEN, W. C. S. (1990). A correlation inequality and a Poisson limit theorem for nonoverlapping balanced subgraphs of a random graph. Random Structures Algorithms 1 231-242.
    • (1990) Random Structures Algorithms , vol.1 , pp. 231-242
    • Suen, W.C.S.1
  • 61
    • 84980191593 scopus 로고
    • Das problem der iterationen
    • VON MISES, R. (1921). Das Problem der Iterationen. Z. Angew. Math. Mech. 1 298-307.
    • (1921) Z. Angew. Math. Mech. , vol.1 , pp. 298-307
    • Von Mises, R.1
  • 63
    • 0007206527 scopus 로고
    • Asymptotic distribution of runs up and down
    • WOLFOWITZ, J. (1944). Asymptotic distribution of runs up and down. Ann. Math. Statist. 15 163-172.
    • (1944) Ann. Math. Statist. , vol.15 , pp. 163-172
    • Wolfowitz, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.