Exact distribution of word occurrences in a random sequence of letters

Journal of Applied Probability

Volumn 36, Issue 1, 1999, Pages 179-193

  Robin, S ^a   Daudin, J J ^a  

^a AGROPARISTECH   (France)

Author keywords

Distance between occurrences; Genome sequence analysis; Markov chain; Patterns; Waiting time

Indexed keywords

EID: 0033238297     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200016958     Document Type: Article

References (20)

1. AKI, S. AND HIRANO, K. (1993). Discrete distributions related to succession events in a two state Markov chain. In Statistical Science and Data Analysis, ed. K. Matusita, M. L. Puri and T. Ahayakawa. WSP International Science Publishers, Zeist, pp. 467-474.
2. BLOM, G. (1982). On the mean number of random digits until a given sequence occurs. J. Appl. Prob. 19, 136-143.
3. BLOM, G. AND THORBURN D. (1982). How many random digits are required until given sequences are obtained? J. Appl. Prob. 19, 518-531.
4. CHRYSAPHINOU, O. AND PAPASTAVRIDIS, S. (1990). The occurrence of sequence patterns in repeated dependent experiments. Theory Prob. Appl. 35, 145-152.
5. COWAN, R. (1991). Expected frequencies of DNA patterns using Whittle's formula. J. Appl. Prob. 28, 886-892.
6. FELLER, W. (1968). An Introduction to Probability Theory and its Applications. Vol I, 3rd edn. Wiley, New York.
7. GESKE, M. X., GODBOLE, A. P., SCHAFFNER, A. A., SKOLNICK, A. M. AND WALLSTROM, G. L. (1995). Compound Poisson approximation for word patterns under Markovian hypothesis. J. Appl. Prob. 32, 877-892.
8. GODBOLE, A. P. (1991). Poisson approximations for runs and patterns of rare events. Adv. Appl. Prob. 23, 851-865.
9. HENAUT, A., ROUXEL, T., GLEIZES A., MOSZER, I. AND DANCHIN, A. (1996). Uneven distribution of GATC motifs in the Escherichia coli chromosome, its plasmids and its phages. J. Mol. Biol. 257, 574-585.
10. JOHNSON N. L., KOTZ S. AND KEMP A. W. (1992). Univariate Discrete Distributions. Wiley, New York.
11. KARLIN, S. AND MACKEN C. (1991). Some statistical problems in the assessment of inhomogeneities of DNA sequence data. J. Amer. Statist. Soc. 86, 27-35.
12. KOUTRAS, M. V. (1997). Waiting time distributions associated with runs of fixed length in two state Markov chains. Ann. Inst. Statist. Math. 49, 123-139.
13. MORI, T. F. (1989). On the number of different patterns preceding a given one. Studia. Sci. Math. Hung. 24, 355-364.
14. PEKOZ, E. A. (1996). Stein's method for geometric approximation. J. Appl. Prob. 33, 707-713.
15. PHILIPPOU, A. N., GEORGHIOU, C. AND PHILIPPOU, G. N. (1983). A generalized geometric distribution and some of its properties. Statist. Prob. Lett. 1, 171-175.
16. PRUM, B., RODOLPHE, F. AND DE TURKHEIM, E. (1995). Finding words with unexpected frequencies in deoxyribonucleic acid sequences. J. R. Statist. Soc. B 57, 205-220.
17. RUDANDER, J. (1996). On the first occurrence of a given pattern in a semi-Markov process. Uppsala Dissertations in Math. 2, Uppsala University, Sweden.
18. SCHBATH, S. (1995). Compound Poisson approximation of word counts in DNA sequences. ESAIM Prob. Statist., 1, 1-16.
19. SCHWAGER, S. (1983). Run probabilities in sequences of Markov dependent trials. J. Amer. Statist. Assoc., 78, 168-175.
20. UCHIDA, M. AND AKI, S. (1995). Sooner or later waiting time problems in a two-state Markov chain. Ann. Inst. Statist. Math. 47, 415-433.