Gamma-distribution order statistics, maximal multinomial frequency and randomization designs

Journal of Statistical Planning and Inference

Volumn 136, Issue 7 SPEC. ISS., 2006, Pages 2213-2226

  Rukhin, Andrew L ^a,b  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^b NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

Banach match box problem; Birthday problem; Clinical trials; Combinatorial extreme value theory; Load balancing; Multinomial trials; Normal order statistics; Poisson approximation; Probability generating function; Renewal process

Indexed keywords

EID: 33644917715     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2005.08.027     Document Type: Article

References (26)

1. K. Anderson M. Sobel R.R. Uppuluri Quota fulfillment times Can. J. Statist. 10 1982 73-88
2. B.C. Arnold N. Balakrishnan N.H. Nagaraja A First Course in Order Statistics 1993 Wiley New York
3. R. Arratia L. Goldstein L. Gordon Poisson approximation and the Chen-Stein method Statist. Sci. 5 1990 403-434
4. Avigdor, N.A., 2002. Building a scalable and reliable parallel file system using commodity computers. Ph.D. Thesis, Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County Campus.
5. A.D. Barbour L. Holst S. Janson Poisson Approximation 1992 Clarendon Press Oxford
6. D. Blackwell J.L. Hodges Jr. Design for the control of selection bias Ann. Math. Statist. 28 1957 449-460
7. G. Blom L. Holst D. Sandell Problems and Snapshots from the World of Probability 1994 Springer New York
8. R.C. Bose S.S. Gupta Moments of order statistics from a normal population Biometrika 46 1959 433-440
9. T. Cacoullos M. Sobel An inverse sampling procedure for selecting the most probable event in a multinomial distribution P.R. Krishnaiah Proceedings of the International Symposium on Multivariate Analysis 1966 Academic Press New York 423-444
10. F.N. David D.E. Barton Combinatorial Chance 1962 Hafner Publishing Co New York
11. P. Diaconis R.L. Graham The analysis of sequential experiments with feedback to subjects Ann. Statist. 9 1981 3-23
12. W. Feller An Introduction to Probability Theory and Its Applications vol. I 1968 Wiley New York
13. E.J. Gumbel Statistics of Extremes 1958 Columbia University Press New York
14. S.S. Gupta Order statistics from the gamma distribution Technometrics 2 1960 243-262
15. L. Holst On birthday, collectors', occupancy and other classical urn problems Internat. Statist. Rev. 54 1986 15-27
16. L. Holst A note on Banach match box problem Statist. Probab. Lett. 8 1989 441-443
17. G.I. Ivchenko On extremal values of samples, Trudy Moscow Instituta Elektron Machinostr. 32 1973 12-31
18. N.L. Johnson D.H. Young Some applications of two approximations to the multinomial distribution Biometrika 47 1960 463-469
19. V.F. Kolchin B.A. Sevast'yanov V.P. Chistyakov Random Allocations 1978 Whinston Sons Washington, DC
20. B. Levin A representation for multinomial cumulative distribution function Ann. Statist. 9 1981 1123-1126
21. B. Levin On calculations involving the maximum cell frequency Commun. Statist. Theory Methods 12 1983 1299-1327
22. C.L. Mallows An inequality involving multinomial probabilities Biometrika 55 1968 422-424
23. J. Riordan An Introduction to Combinatorial Analysis 1958 Wiley New York
24. W.F. Rosenberger J.M. Lachin Randomization in Clinical Trials: Theory and Practice 2002 Wiley New York
25. N.M. Temme Asymptotic inversion of incomplete gamma function Math. Comput. 68 1992 755-764
26. R.R. Uppuluri J. Blot A probability distribution arising in a riff-shuffle G.P. Patil Random Counts in Scientific Work 1970 Pennsylvania State University Press University Park