Probabilistic transforms for combinatorial urn models

Combinatorics Probability and Computing

Volumn 13, Issue 4-5, 2004, Pages 645-675

  Milenkovic, O ^a   Compton, K J ^b  

^a UCB 450   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; INTEGRATION; PARAMETER ESTIMATION; POISSON EQUATION; PROBABILITY;

HOMOGENEOUS FUNCTIONS; LOG-CONCAVE; NEGATIVE-BINOMIAL TRANSFORM; NONNEGATIVE INTEGERS;

MATHEMATICAL TRANSFORMATIONS;

EID: 5044246498     PISSN: 09635483     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0963548304006285     Document Type: Conference Paper

References (43)

1. Abramowitz, M. and Stegun, I. (1964) Handbook of Mathematical Functions, Dover, New York.
2. Alajaji, F. and Fuja, T. (1994) A communication channel modeled on contagion. IEEE Trans. Inform. Theory 40 2035-2041.
3. Andrews, G. (1984) The Theory of Partitions, Cambridge University Press.
4. Apostol, T. (1990) Modular Functions and Dirichlet Series in Number Theory, Springer, New York.
5. Arratia, R. and Tavare, S. (1994) Independent process approximations for random combinatorial structures. Adv. Math. 104 90-154.
6. Asai, N., Kubo, I. and Kuo, H. H. (2000) Bell numbers, log-concavity and log-convexity. Acta Applicandae Mathematicae 63 79-87.
7. Bender, E. and Canfield, R. (1995) Log-concavity and related properties of the cycle index polynomials. J. Combin. Theory Ser. A 74 55-70.
8. Billingsley, P. (1995) Probability and Measure, Series in Probability and Mathematical Statistics, Wiley, New York.
9. Burris, S. (2001) Density in Number Systems, Vol. 86 of Mathematical Surveys and Monographs, AMS.
10. Compton, K. J. (1987) Some methods for computing component distribution probabilities in relational structures. Discrete Math. 66 59-77.
11. De Bruijn, N. (1981) Asymptotic Methods in Analysis, Dover, New York.
12. Drmota, M., Gardy, D. and Gittenberger, B. (2004) General urn models with several types of balls and Gaussian limiting fields. Random Struct. Alg. 24 75-103.
13. Drmota, M., Gardy, D. and Gittenberger, B. (2001) A unified presentation of some urn models. Algorithmica 29 120-147.
14. Eramo, V., Listanti, M., Nuzman, C. and Whiting, P. (2002) Optical switch dimensioning and the classical occupancy problem. Int. J. Communication Systems 15 127-141.
15. Feller, W. (1967) An Introduction to Probability Theory and its Applications, Vol. I, Wiley, New York.
16. Feller, W. (1967) An Introduction to Probability Theory and its Applications, Vol. II, Wiley, New York.
17. Flajolet, P. and Odlyzko, A. (1990) Singularity analysis of generating functions. SIAM J. Discrete Math. 3 216-240.
18. Fristedt, B. (1993) The structure of random partitions of large integers. Trans. Amer. Math. Soc. 337 703-735.
19. Gonnet, G. H. and Munro, J. I. (1984) The analysis of linear probing sort by the use of a new mathematical transform. J. Algorithms 5 451-470.
20. Hardy, G. H. (1949) Divergent Series, Clarendon Press, Oxford.
21. Hofri, M. (1995) Analysis of Algorithms: Computational Methods and Mathematical Tools, Oxford University Press.
22. Holst, L. The Poisson-Dirichlet distribution and its relatives revisited. In revision.
23. Jacquet, P. and Szpankowski, W. (1995) Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees. Theoret. Comput. Sci. 144 161-197.
24. Johnson, N. L. and Kotz, S. (1977) Urn Models and Their Application: An Approach to Modern Discrete Probability, Wiley, New York.
25. Khinchin, A. Y. (1950) On the analytical apparatus of physical statistics. Trudy Mat. Inst. Steklov 33.
26. Kolchin, V. (1986) Random Mappings, Optimization Software Inc. Publishing Company.
27. Kolchin, V., Sevast'yanov, B. and Chistyakov, V. (1978) Random Allocations, Wiley, New York.
28. Milenkovic, O. and Compton, K. J. (2003) Probabilistic analysis of Gosper's algorithm. Submitted to Algorithmica. Available at http://ece.colorado. edu/~milenkov/.
29. Extended version of [28], Available at http://ece.colorado.edu/~milenkov/ .
30. Nehari, Z. (1961) Introduction to Complex Analysis, Allyn and Bacon, Boston.
31. Nuzman, C. and Whiting, P. (2001) Calculus of variations and sample path large deviations and the classical occupancy problem. In Allerton Conf. on Commun., Comp., and Control.
32. Odlyzko, A. and Flajolet, P. (1995) Asymptotic enumeration methods. In Handbook of Combinatorics, 1, Elsevier, Amsterdam, pp. 1063-1229.
33. Poblete, P. V., Munro, J. I. and Papadakis, T. (1995) The binomial transform and its applications to the analysis of skip lists. In Proc. 3rd European Symposium on Algorithms, ESA95, Corfu, Greece, Vol. 979 of Lecture Notes in Computer Science, Springer.
34. Shepp, L. A. and Lloyd, S. P. (1966) Ordered cycle lengths in a random permutation. Trans. Amer. Math. Soc. 121 340-357.
35. Simha, R. and Majumdar, A. An urn model with applications to database performance evaluation. In submission.
36. Stanley, R. (1997) Enumerative Combinatorics, Vol. 1, Cambridge University Press.
37. Stanley, R. (1999) Enumerative Combinatorics, Vol. 2, Cambridge University Press.
38. Szpankowski, W. (2001) Average Case Analysis of Algorithms on Sequences, Wiley, New York.
39. Temme, N. (1993) Asymptotic estimates of Stirling numbers. Studies in Applied Mathematics 89 233-243.
40. Warde, W. D. and Katti, S. K (1964) Infinite divisibility of discrete distributions II. Ann. Math. Stat. 42 1088-1090.
41. Wilf, H. (1994) Generatingfunctionology, Academic Press, Boston.
42. Wong, E., Chan, A. and Yum, P. (2000) Analysis of rerouting in circuit-switched networks. IEEE/ACM Trans. Networking 8 (June).
43. Woods, A. R. (1997) Counting finite models. J. Symbolic Logic 62 925-949.