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Volumn 7, Issue 3, 1997, Pages 666-678

Explicit distributional results in pattern formation

Author keywords

Exponential family; Markov chain; Run; Stopping time

Indexed keywords


EID: 0031526698     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034801248     Document Type: Article
Times cited : (41)

References (26)
  • 1
    • 0012153450 scopus 로고
    • Distributions of numbers of failures and successes until the first consecutive k successes
    • AKI, S. and HIRANO, K. (1994). Distributions of numbers of failures and successes until the first consecutive k successes. Ann. Inst. Statist. Math. 46 193-202.
    • (1994) Ann. Inst. Statist. Math. , vol.46 , pp. 193-202
    • Aki, S.1    Hirano, K.2
  • 2
    • 0038134184 scopus 로고
    • Joint distributions of numbers of success-runs and failures until the first consecutive k successes
    • AKI, S. and HIRANO, K. (1995). Joint distributions of numbers of success-runs and failures until the first consecutive k successes. Ann. Inst. Statist. Math. 47 225-235.
    • (1995) Ann. Inst. Statist. Math. , vol.47 , pp. 225-235
    • Aki, S.1    Hirano, K.2
  • 3
    • 0039175127 scopus 로고
    • Pattern recognition in Markov chains
    • (A. P. Godbole and S. G. Papastavridis, eds.) Kluwer, Dordrecht
    • BANJEVIC, D. (1994). Pattern recognition in Markov chains. In Runs and Patterns in Probability (A. P. Godbole and S. G. Papastavridis, eds.) 213-230. Kluwer, Dordrecht.
    • (1994) Runs and Patterns in Probability , pp. 213-230
    • Banjevic, D.1
  • 5
    • 0000883264 scopus 로고
    • Conditionality resolutions
    • BARNDORFF-NIELSEN, O. (1980). Conditionality resolutions. Biometrika 67 293-310.
    • (1980) Biometrika , vol.67 , pp. 293-310
    • Barndorff-Nielsen, O.1
  • 6
    • 0001616513 scopus 로고
    • Markov renewal processes, counters and repeated sequences in Markov chains
    • BIGGINS, J. D. and CANNINGS, C. (1987). Markov renewal processes, counters and repeated sequences in Markov chains. Adv. in Appl. Probab. 19 521-545.
    • (1987) Adv. in Appl. Probab. , vol.19 , pp. 521-545
    • Biggins, J.D.1    Cannings, C.2
  • 8
    • 0020179938 scopus 로고
    • How many random digits are required until given sequences are obtained?
    • BLOM, G. and THORBURN, D. (1982). How many random digits are required until given sequences are obtained? J. Appl. Probab. 19 518-531.
    • (1982) J. Appl. Probab. , vol.19 , pp. 518-531
    • Blom, G.1    Thorburn, D.2
  • 9
  • 11
    • 0001766090 scopus 로고
    • A limit theorem on the number of overlapping appearances of a pattern in a sequence of independent trials
    • CHRYSSAPHINOU, O. and PAPASTAVRIDIS, S. (1988). A limit theorem on 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
  • 12
    • 0001800887 scopus 로고
    • The occurrence of a sequence of patterns in repeated dependent experiments
    • CHRYSSAPHINOU, O. and PAPASTAVRIDIS, S. (1990). The occurrence of a sequence of patterns in repeated dependent experiments. Theory Probab. Appl. 35 167-173.
    • (1990) Theory Probab. Appl. , vol.35 , pp. 167-173
    • Chryssaphinou, O.1    Papastavridis, S.2
  • 14
    • 84950460234 scopus 로고
    • Distribution theory of runs: A markov chain approach
    • FU, J. C. and KOUTRAS, M. V. (1994). Distribution theory of runs: a Markov chain approach. J. Amer. Statist. Assoc. 89 1050-1058.
    • (1994) J. Amer. Statist. Assoc. , vol.89 , pp. 1050-1058
    • Fu, J.C.1    Koutras, M.V.2
  • 16
    • 0013695809 scopus 로고
    • The occurrence of sequence patterns in repeated experiments and hitting times in a Markov chain
    • GERBER, H. and LI, S-Y. R. (1981). The occurrence of sequence patterns in repeated experiments and hitting times in a Markov chain. Stochastic Process. Appl. 11 101-108.
    • (1981) Stochastic Process. Appl. , vol.11 , pp. 101-108
    • Gerber, H.1    Li, S.-Y.R.2
  • 17
    • 0002845889 scopus 로고
    • Improved poisson approximation for word patterns
    • GODBOLE, A. P. and SCHAEFFNER, A. A. (1993). Improved Poisson approximation for word patterns. Adv. in Appl. Probab. 25 334-347.
    • (1993) Adv. in Appl. Probab. , vol.25 , pp. 334-347
    • Godbole, A.P.1    Schaeffner, A.A.2
  • 18
    • 0000827892 scopus 로고
    • Long repetitive patterns in random sequences
    • GUIBAS, L. J. and ODLYZKO, A. M. (1980). Long repetitive patterns in random sequences. Z. Wahrsch. Verw. Gebiete 53 241-262.
    • (1980) Z. Wahrsch. Verw. Gebiete , vol.53 , pp. 241-262
    • Guibas, L.J.1    Odlyzko, A.M.2
  • 19
    • 34250201608 scopus 로고
    • String overlaps, pattern matching, and nontransitive games
    • GUIBAS, L. J. and ODLYZKO, A. M. (1981). String overlaps, pattern matching, and nontransitive games. J. Combin. Theory A 30 183-208.
    • (1981) J. Combin. Theory A , vol.30 , pp. 183-208
    • Guibas, L.J.1    Odlyzko, A.M.2
  • 20
    • 0001530766 scopus 로고
    • A martingale approach to the study of occurrence of sequence patterns in repeated experiments
    • LI, S-Y. R. (1980). A martingale approach to the study of occurrence of sequence patterns in repeated experiments. Ann. Probab. 8 1171-1176.
    • (1980) Ann. Probab. , vol.8 , pp. 1171-1176
    • Li, S.-Y.R.1
  • 21
    • 38249022168 scopus 로고
    • On binomial distributions of order k
    • LING, K. D. (1988). On binomial distributions of order k. Statist. Probab. Lett. 6 247-250.
    • (1988) Statist. Probab. Lett. , vol.6 , pp. 247-250
    • Ling, K.D.1
  • 22
    • 0037967195 scopus 로고
    • Success runs of length k in Markov dependent trials
    • MOHANTY, S. G. (1994). Success runs of length k in Markov dependent trials. Ann. Inst. Statist. Math. 46 777-796.
    • (1994) Ann. Inst. Statist. Math. , vol.46 , pp. 777-796
    • Mohanty, S.G.1
  • 23
    • 0001450383 scopus 로고
    • The distribution theory of runs
    • MOOD, A. M. (1940). The distribution theory of runs. Ann. Math. Statist. 11 367-392.
    • (1940) Ann. Math. Statist. , vol.11 , pp. 367-392
    • Mood, A.M.1
  • 24
    • 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: Probability and Statistics 1 1-16.
    • (1995) ESAIM: Probability and Statistics , vol.1 , pp. 1-16
    • Schbath, S.1
  • 25
    • 0000498715 scopus 로고
    • Noncurved exponential families associated with observations over finite state Markov chains
    • STEFANOV, V. T. (1991). Noncurved exponential families associated with observations over finite state Markov chains. Scand J. Statist. 18 353-356.
    • (1991) Scand J. Statist. , vol.18 , pp. 353-356
    • Stefanov, V.T.1
  • 26
    • 21844504083 scopus 로고
    • Explicit limit results for minimal sufficient statistics and maximum likelihood estimators in some Markov processes: Exponential families approach
    • STEFANOV, V. T. (1995). Explicit limit results for minimal sufficient statistics and maximum likelihood estimators in some Markov processes: exponential families approach. Ann. Statist. 23 1073-1101.
    • (1995) Ann. Statist. , vol.23 , pp. 1073-1101
    • Stefanov, V.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.