Compound Poisson approximation of word counts in DNA sequences

Sophie Schbath

ESAIM: Probability and Statistics (1997)

  • Volume: 1, page 1-16
  • ISSN: 1292-8100

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Schbath, Sophie. "Compound Poisson approximation of word counts in DNA sequences." ESAIM: Probability and Statistics 1 (1997): 1-16. <http://eudml.org/doc/104232>.

@article{Schbath1997,
author = {Schbath, Sophie},
journal = {ESAIM: Probability and Statistics},
keywords = {DNA sequences; word counts; Poisson approximations; compound Poisson distribution; Chen-Stein method; Markov chains; word periods},
language = {eng},
pages = {1-16},
publisher = {EDP Sciences},
title = {Compound Poisson approximation of word counts in DNA sequences},
url = {http://eudml.org/doc/104232},
volume = {1},
year = {1997},
}

TY - JOUR
AU - Schbath, Sophie
TI - Compound Poisson approximation of word counts in DNA sequences
JO - ESAIM: Probability and Statistics
PY - 1997
PB - EDP Sciences
VL - 1
SP - 1
EP - 16
LA - eng
KW - DNA sequences; word counts; Poisson approximations; compound Poisson distribution; Chen-Stein method; Markov chains; word periods
UR - http://eudml.org/doc/104232
ER -

References

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  6. CHRYSSAPHINOU, O. and PAPASTAVRIDIS, S. ( 1988a). A limit theorem for the number of non-overlapping occurrences of a pattern in a sequence of independent trials. J. Appl. Prob. 25 428-431. Zbl0643.60020MR938208
  7. CHRYSSAPHINOU, O. and PAPASTAVRIDIS, S. ( 1988b). A limit theorem on the number of overlapping appearances of a pattern in a sequence of independent trials. Prob. Theory Rel. Fields. 79 129-143. Zbl0631.60027MR952999
  8. DOUKHAN, P. ( 1994). Mixing: Properties and Examples. L.N.S. 85, Springer-Verlag. Zbl0801.60027MR1312160
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  10. GESKE, M. X., GODBOLE, A. P., SCHAFFNER, A. A., SKOLNICK, A. M. and WALLSTROM, G. L. ( 1995). Compound Poisson approximations for word patterns under Markovian hypotheses. J. Appl. Prob. To appear. Zbl0843.60025MR1363330
  11. GODBOLE, A. P. ( 1991). Poisson approximations for runs and patterns of rare events. Adv. Appl. Prob. 23 851-865. Zbl0751.60018MR1133732
  12. GODBOLE, A. P. and SCHAFFNER, A. A. ( 1993). Improved poisson approximations for word patterns. Adv. Appl. Prob. 25 334-347. Zbl0772.60013MR1212615
  13. GUIBAS, L. J. and ODLYZKO, A. M. ( 1981). Periods in strings. J. Combinatorial Theory A. 30 19-42. Zbl0464.68070MR607037
  14. HIRANO, K. and AKI, S. ( 1993). On number of occurrences of sucess runs of specified length in a two-state Markov chain. Statistica Sinica. 3 313-320. Zbl0822.60061MR1243389
  15. KARLIN, S. and OST, F. ( 1987). Counts of long aligned word matches among random letter sequences. Ann. Prob. 19 293-351. Zbl0621.60074MR820431
  16. LOTHAIRE, M. ( 1983). Combinatorics on words. Addison-Wesley. Zbl0514.20045MR675953
  17. PRUM, B., RODOLPHE, F. and TURCKHEIM, É.DE ( 1995). Finding words with unexpected frequencies in DNA sequences. J. R. Statist. Soc. B. 57 205-220. Zbl0817.92012MR1325386
  18. ROOS, M. ( 1994). Stein's method for compound Poisson approximation : the local approach. Ann. Appl. Prob. 4 1177-1187. Zbl0816.60021MR1304780
  19. SCHBATH, S. ( 1995). Étude asymptotique du nombre d'occurrences d'un mot dans une chaîne de Markov et application à la recherche de mots de fréquence exceptionnelle dans les séquences d'ADN. PhD thesis, Université René Descartes, Paris V. 
  20. SCHBATH, S., PRUM, B. and TURCKHEIM, É. DE ( 1995). Exceptional motifs in different Markov chain models for a statistical analysis of DNA sequences. J. Comp. Biol. 2 417-437. 
  21. TRIFONOV, E. N. ( 1989). The multiple codes of nucleotide sequences. Bull. Math. Biol. 51 417-432. Zbl0674.92011MR958154

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