New approximations for the distribution of the r -scan statistic

Statistics and Probability Letters

Volumn 46, Issue 4, 2000, Pages 411-419

  Su, Xiaoping ^a   Wallenstein, Sylvan ^a  

^a MOUNT SINAI SCHOOL OF MEDICINE   (United States)

Author keywords

Compound Poisson approximation; Declumping; P lya Aeppli distribution

Indexed keywords

EID: 0041777869     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(99)00135-2     Document Type: Article

References (16)

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: A. Gut, L. Holst (Eds.), Probability and Mathematical Statistics, Essays in honour of Carl-Gustave Esseen, Uppsalla University, pp. 1-10.
3. Alm S.E. On the distribution of scan statistics of a two-dimensional Poisson process. Adv. Appl. Probab. 29:1997;1-18.
4. Arratia R., Goldstein L., Gordon L. Poisson approximation and the Chen-Stein method. Statist. Sci. 5:1990;403-434.
5. Berman M., Eagleson G.K. A useful upper bound for the tail probabilities when the sample size is large. J. Amer. Statist. Assoc. 80:1985;886-889.
6. Dembo A., Karlin S. Poisson approximations for. r -scan process Ann. Appl. Probab. 2:1992;329-357.
7. Glaz J. Approximations for the tail probabilities and moments of the scan statistic. Statist. Med. 12:1993;1845-1852.
8. Glaz J., Naus J., Roos M., Wallenstein S. Poisson approximations for the distribution and moments of ordered. m -spacings Ann. Appl. Probab. 4:1994;271-281.
9. Huffer F.W., Lin C.T. Approximating the distribution of the scan statistic using moments of the number of clumps. J. Amer. Statist. Assoc. 92:1997;1466-1475.
10. Johnson, N.L., Kotz, S., Kemp, A.W., 1992. Univariate Discrete Distributions. Wiley, New York.
11. Karlin S., Macken C. Some statistical problems in the assessment of inhomogeneities of DNA sequence data. J. Amer. Statist. Assoc. 86:1991;27-35.
12. Naus J.I. Approximations for distributions of scan statistics. J. Amer. Statist. Assoc. 77:1982;177-183.
13. Newell, G.F., 1963. Distribution for the smallest distance between any pair of k th nearest-neighbor random points on a line. Time Series Analysis, Proceedings of a Conference, Brown Univ., pp. 89-103.
14. Roos M. Compound Poisson approximations for the numbers of extreme spacings. Adv. Appl. Probab. 25:1993;847-874.
15. Sherbrooke C.C. Discrete compound Poisson processes and tables of the geometric Poisson distribution. Naval Res. Logist. Quart. 15:1968;189-203.
16. Su, X., Wallenstein, S., 1999. New approximations for the distribution of the r -scan statistic. Technical Report, Mount Sinai School of Medicine.