Limit distribution of the number of consecutive records

Random Structures and Algorithms

Volumn 26, Issue 4, 2005, Pages 404-417

  Chern, Hua Huai ^a   Hwang, Hsien Kuei ^b  

^a NATIONAL TAIWAN OCEAN UNIVERSITY   (Taiwan)

^b INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22944490576     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/rsa.20052     Document Type: Article

References (16)

1. B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, Records, Wiley, New York, 1998.
2. R. Arratia, A. D. Barbour, and S. Tavaré, Logarithmic combinatorial structures: A probabilistic approach, European Mathematical Society Publishing House, Zürich, 2003.
3. J. Bunge and C. M. Goldie, "Record sequences and their applications," Stochastic processes: theory and methods, Handbook of Statistics 19, 277-308 North-Holland, Amsterdam, 2001.
4. K. N. Chandler, The distribution and frequency of record values, J R Stat Soc Ser B Methodol 14 (1952), 220-228.
5. H.-H. Chern and H.-K. Hwang, Partial match queries in random k-d trees, Preprint, 2003, http://algo.stat.sinica.edu.tw
6. H.-H. Chern, H.-K. Hwang, and T.-H. Tsai, An asymptotic theory for Cauchy Euler differential equations with applications to the analysis of algorithms, J Algorithms 44 (2002), 177-255.
7. H.-H. Chern, H.-K. Hwang, and Y.-N. Yeh, Distributions of the number of consecutive records, Random Structures Algorithms 17 (2000), 169-196.
8. E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955.
9. S. Elizalde and M. Noy, Consecutive patterns in permutations, Adv Appl Math 30 (2003), 110-125.
10. A. Erdélyi, Higher transcendental functions, Volume I, Krieger, Malabar, FL, 1953.
11. S. Gulati and W. J. Padgett, Parametric and nonparametric inference from record-breaking data, Lecture Notes in Statistics 172, Springer, New York, 2003.
12. H.-K. Hwang, Asymptotics of Poisson approximation to random discrete distributions: An analytic approach, Adv Appl Probab 31 (1999), 448-491.
13. B.C. Johnson, The distribution of increasing 2-sequences in random permutations of arbitrary multi-sets, Stat Probab Lett 59 (2002), 67-74.
14. A. van der Poorten, A proof that Euler missed ... Apéry's proof of the irrationality of f (3). An informal report. Math Intelligencer 1 (1978/79), 195-203.
15. J. Wimp and D. Zeilberger, Resurrecting the asymptotics of linear recurrences. J Math Anal Appl 111 (1985), 162-176.
16. W. Zudilin, An Apéry-like difference equation for Catalan's constant, Electron J Combin 10 (R14) (2003), 10 pages, http://www.combinatorics.org/Volume_10/PDF/v10i1r14.pdf.