Limit theorem for maximal segmental score for random sequences of random length
Authors:
B. L. S. Prakasa Rao and M. Sreehari
Journal:
Theor. Probability and Math. Statist. 76 (2008), 155-158
MSC (2000):
Primary 60G50
DOI:
https://doi.org/10.1090/S0094-9000-08-00739-4
Published electronically:
July 16, 2008
MathSciNet review:
2368747
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We obtain the limiting distribution of the maximal segmental score for the partial sums for a random number of independent and identically distributed random variables.
References
- R. Arratia, L. Gordon, and M. S. Waterman, The Erdős-Rényi law in distribution, for coin tossing and sequence matching, Ann. Statist. 18 (1990), no. 2, 539–570. MR 1056326, DOI https://doi.org/10.1214/aos/1176347615
- Richard Arratia and Michael S. Waterman, A phase transition for the score in matching random sequences allowing deletions, Ann. Appl. Probab. 4 (1994), no. 1, 200–225. MR 1258181
- O. Barndorff-Nielsen, On the limit distribution of the maximum of a random number of independent random variables, Acta Math. Acad. Sci. Hungar. 15 (1964), 399–403. MR 170360, DOI https://doi.org/10.1007/BF01897148
- S. Csörgő, On limit distributions of sequences of random variables with random indices, Acta Math. Acad. Sci. Hungar. 25 (1974), 227–232. MR 365660, DOI https://doi.org/10.1007/BF01886078
- Donald L. Iglehart, Extreme values in the $GI/G/1$ queue, Ann. Math. Statist. 43 (1972), 627–635. MR 305498, DOI https://doi.org/10.1214/aoms/1177692642
- Samuel Karlin and Amir Dembo, Limit distributions of maximal segmental score among Markov-dependent partial sums, Adv. in Appl. Probab. 24 (1992), no. 1, 113–140. MR 1146522, DOI https://doi.org/10.2307/1427732
- S. Mercier and J. J. Daudin, Exact distribution for the local score of one i.i.d. random sequence, J. Comput. Biol. 8 (2001), 373–380.
- S. Mercier, D. Cellier, and D. Charlot, An improved approximation for assessing the statistical significance of molecular sequence features, J. Appl. Probab. 40 (2003), no. 2, 427–441. MR 1978101, DOI https://doi.org/10.1017/s0021900200019409
References
- R. Arratia, L. Gordon, and M. S. Waterman, The Erdös–Rényi law in distribution, for coin tossing and sequence matching, Ann. Statist. 18 (1990), 539–570. MR 1056326 (92a:60054)
- R. Arratia and M. S. Waterman, A phase transition for the score in matching random sequences allowing deletions, Ann. Appl. Prob. 4 (1994), 200–225. MR 1258181 (95b:60024)
- O. Barndorff-Nielsen, On the limit distribution of the maximum of a random number of independent random variables, Acta Math. Acad. Sci. Hungar. 15 (1964), 399–403. MR 0170360 (30:598)
- S. Csörgö, On limit distributions of sequences of random variables with random indices, Acta Math. Acad. Sci. Hungar. 25 (1974), 227–232. MR 0365660 (51:1912)
- D. L. Iglehart, Extreme values in the GI/G/1 queue, Ann. Math. Statist. 43 (1972), 627–635. MR 0305498 (46:4628)
- S. Karlin and A. Dembo, Limit distributions of maximal segmental score among Markov-dependent partial sums, Adv. Appl. Probab. 24 (1992), 113–140. MR 1146522 (93b:60042)
- S. Mercier and J. J. Daudin, Exact distribution for the local score of one i.i.d. random sequence, J. Comput. Biol. 8 (2001), 373–380.
- S. Mercier, D. Cellier, and D. Charlot, An improved approximation for assessing the statistical significance of molecular sequence features, J. Appl. Probab. 40 (2003), 427–441. MR 1978101 (2004d:60115)
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2000):
60G50
Retrieve articles in all journals
with MSC (2000):
60G50
Additional Information
B. L. S. Prakasa Rao
Affiliation:
University of Hyderabad, Hyderabad 500046, India
Email:
blsprsm@uohyd.ernet.in
M. Sreehari
Affiliation:
M. S. University, Vadodara, India
Email:
msreehari03@yahoo.co.uk
Keywords:
Maximum segmental score,
limit theorem,
random sequences,
random length
Received by editor(s):
July 17, 2006
Published electronically:
July 16, 2008
Article copyright:
© Copyright 2008
American Mathematical Society
