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

  • Rukhin A
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The paper discusses the relationship between the gamma-distribution order statistics, the maximal cell frequency in multinomial trials and the distribution arising in a commonly used balanced randomization scheme with several treatments. The latter is used in clinical trials, load balancing in computer files storage, parapsychological experiments, etc., where a randomization design starts with the uniform probability assignment of subjects to treatments. The limiting distributions of the waiting time until a treatment receives the given number of subjects are described. The relationship to classical occupancy problems, in particular, to the Banach match-box problem and to the birthday problem is discussed. © 2005 Elsevier B.V. All rights reserved.

Author-supplied 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

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  • Andrew L. Rukhin

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