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Références bibliographiques / Bibliography


Mot-clé: word counts

[1] Chryssaphinou, O., and Papastavridis, S. A limit theorem for the number of non-overlapping occurrences of a pattern in a sequence of independent trials. J. Appl. Prob. 25 (1988), 428-431.

[2] Chryssaphinou, O., and Papastavridis, S. A limit theorem on the number of overlapping appearances of a pattern in a sequence of independent trials. Prob. Theory Rel. Fields 79 (1988), 129-143.

[3] Chryssaphinou, O., and Papastavridis, S. On the number of overlapping success runs in a sequence of independent bernoulli trials. Application of Fibonacci Numbers 5 (1993), 103-112.

[4] Cowan, R. Expected frequencies of DNA patterns using Whittle's formula. J. Appl. Prob. 28 (1991), 886-892.

[5] Erhardsson, T. Compound Poisson approximation for Markov chains. PhD thesis, Royal Institute of Technology, Stockholm, 1997.

[6] Fu, J. C., and Koutras, V. Distribution theory of runs: A Markov chain approach. J. Amer. Statist. Soc. 89 (1994), 1050-1058.

[7] Geske, M. X., Godbole, A. P., Schaffner, A. A., Skolnick, A. M., and Wallstrom, G. L. Compound Poisson approximations for word patterns under Markovian hypotheses. J. Appl. Prob. 32 (1995), 877-892.

[8] Godbole, A. P. Specific formula for some success run distributions. Statist. Prob. Letters 10 (1990), 119-124.

[9] Godbole, A. P. Poisson approximations for runs and patterns of rare events. Adv. Appl. Prob. 23 (1991), 851-865.

[10] Godbole, A. P., and Schaffner, A. A. Improved poisson approximations for word patterns. Adv. Appl. Prob. 25 (1993), 334-347.

[11] Hirano, K., and Aki, S. On number of occurrences of sucess runs of specified length in a two-state Markov chain. Statistica Sinica 3 (1993), 313-320.

[12] Karlin, S., Burge, C., and Campbell, A. M. Statistical analyses of counts and distributions of restriction sites in DNA sequences. Nucl. Acids Res. 20 (1992), 1363-1370.

[13] Kleffe, J., and Borodovsky, M. First and second moment of counts of words in random texts generated by Markov chains. Comp. Applic. Biosci. 8 (1992), 433-441.

[14] Kleffe, J., and Langbecker, U. Exact computation of pattern probabilities in random sequences generated by Markov chains. Comp. Applic. Biosci. 6 (1990), 347-353.

[15] Lundstrom, R. Stochastic models and statistical methods for DNA sequence data. PhD thesis, University of Utah, 1990.

[16] Pevzner, P. A., Borodovsky, M. Y., and Mironov, A. A. Linguistics of nucleotides sequences I: The significance of deviations from mean statistical characteristics and prediction of the frequencies of occurrence of words. J. Biomol. Struct. Dynamics 6 (1989), 1013-1026.

[17] Rajarshi, M. B. Success runs in a two-state Markov chain. J. Appl. Prob. 11 (1974), 190-192.

[18] Reinert, G., and Schbath, S. Compound Poisson and Poisson process approximations for occurrences of multiple words in markov chains. J. Comp. Biol. 5 (1998), 223-254.

[19] Reinert, G., and Schbath, S. Compound Poisson approximations for occurrences of multiple words. In Statistics in Genetics and Molecular Biology, F. Seillier, Ed. IMS Lecture Notes-Monograph Series, 1999. Vol. 33.

[20] Régnier, M., and Szpankowski, W. A last word on frequency of pattern occurrences in a markovian sequence. Submitted to IEEE Transactions on Information Theory , 1996.

[21] Schbath, S. Compound Poisson approximation of word counts in DNA sequences. ESAIM: Probability and Statistics 1 (1995), 1-16.
Available here

[22] Schbath, S. 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, 1995.

[23] Schbath, S. An efficient statistic to detect over- and under-represented words in DNA sequences. J. Comp. Biol. 4 (1997), 189-192.

[24] Schbath, S., Prum, B., and Turckheim, E. d. Exceptional motifs in different Markov chain models for a statistical analysis of DNA sequences. J. Comp. Biol. 2 (1995), 417-437.

[25] Stuckle, E. E., Emmrich, C., Grob, U., and Nielsen, P. J. Statistical analysis of nucleotide sequences. Nucl. Acids Res. 18 (1990), 6641-6647.

[26] Tanushev, M. S. Central limit theorem for several patterns in a markov chain sequence of letters. Preprint, 1996.

[27] Tanushev, M. S., and Arratia, R. Central limit theorem for renewal theory for several patterns. J. Comp. Biol. 4 (1997), 35-44.

Fri Feb 11 09:39:23 MET 2000

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