On Homogeneous Multivariate Distributions in Random Occupancy Models and Their Applications

Kiyoshi Inoue ()
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Kiyoshi Inoue: Seikei University

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 3, 1129-1153

Abstract: Abstract In this article, we consider random occupancy models and the related problems based on the methods of generating functions. The waiting time distributions associated with sequential random occupancy models are investigated through the probability generating functions. We provide the effective computational tools for the evaluation of the probability functions by making use of the Bell polynomials. The results presented here provide a wide framework for developing the theory of occupancy models. Finally, we treat several examples in order to demonstrate how our theoretical results are employed for the investigation of the random occupancy models along with numerical results.

Keywords: Random occupancy models; Urn model; Occupancy numbers; Waiting times; Bell polynomials; Probability function; Probability generating function; Double generating function; Scan statistics; Birthday problem; Coupon collection problem; Pólya urn model.; Primary 62E15; Secondary 60E05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-020-09807-9

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