On the distributions of scan statistics of a two-dimensional Poisson process

Advances in Applied Probability

Volumn 29, Issue 1, 1997, Pages 1-18

  Alm, Sven Erick ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

Approximation; Poisson process; Scan statistic

Indexed keywords

EID: 0003099908     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800027750     Document Type: Article

References (9)

1. ALDOUS, D. (1989) Probability Approximations via the Poisson Clumping Heuristic. Springer, New York.
2. ALM, S. E. (1983) On the distribution of the scan statistic of a Poisson process. In Probability and Mathematical Statistics: Essays in Honour of Carl-Gustav Esseen. ed. A. Gut and L. Holst. pp. 1-10.
3. HUSTINGTON, R. J. and NAUS, J. I. (1975) A simpler expression for kth nearest-neighbor coincidence probabilities. Ann. Prob. 3, 894-896.
4. JANSON, S. (1984) Bounds on the distributions of extremal values of a scanning process. Stoch. Proc. Appl. 18, 313-328.
5. LOADER, C. R. (1991) Large-deviation approximations to the distribution of scan statistics. Adv. Appl. Prob. 23, 751-771.
6. MACK, C. (1949) The expected number of aggregates in a random distribution of n points. Proc. Cambridge Phil. Soc. 46, 285-292.
7. MÅNSSON, M. (1994) Covering uniformly distributed points by convex scanning sets. Preprint 1994:17/ISSN 0347-2809. Chalmers University of Technology.
8. MÅNSSON, M. (1995) Intersections of uniformly distributed translations of convex sets in two and three dimensions. Preprint 1995:11/ISSN 0347-2809. Chalmers University of Technology.
9. NAUS, J. I. (1982) Approximations for distributions of scan statistics. J. Amer. Statist. Assoc. 77, 177-183.