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.
Rukhin, A. L. (2006). Gamma-distribution order statistics, maximal multinomial frequency and randomization designs. Journal of Statistical Planning and Inference, 136(7 SPEC. ISS.), 2213–2226. https://doi.org/10.1016/j.jspi.2005.08.027