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The Sequential Occupancy Problem through Group Throwing of Indistinguishable Balls

Author

Listed:
  • Tamar Gadrich

    (Ort Braude College)

  • Rachel Ravid

    (Ort Braude College)

Abstract

The occupancy problem is generalized to the case where instead of throwing one ball at a time, a fixed size group of indistinguishable balls are distributed sequentially into cells. Bose-Einstein statistics is used for analyzing the distribution of the waiting time until each cell is occupied by at least one ball. Each trial is classified according to its jump size, i.e. the number of newly occupied cells. We propose an approach to decompose the occupancy and filling processes in terms of the jumps sizes using a multi-dimensional representation. A set of recursive equations is built in order to obtain the joint generating probability function of a series of random variables, each of which denotes the number of trials for a given jump size that occurred during the filling process. As a special case, the joint probability function of these random variables is obtained.

Suggested Citation

  • Tamar Gadrich & Rachel Ravid, 2011. "The Sequential Occupancy Problem through Group Throwing of Indistinguishable Balls," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 433-448, June.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:2:d:10.1007_s11009-009-9161-3
    DOI: 10.1007/s11009-009-9161-3
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    References listed on IDEAS

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    1. John E. Kobza & Sheldon H. Jacobson & Diane E. Vaughan, 2007. "A Survey of the Coupon Collector’s Problem with Random Sample Sizes," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 573-584, December.
    2. Paul Dupuis & Jim (Xiao) Zhang & Philip Whiting, 2006. "Refined Large Deviation Asymptotics for the Classical Occupancy Problem," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 467-496, December.
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    Cited by:

    1. Kiyoshi Inoue, 2021. "On Homogeneous Multivariate Distributions in Random Occupancy Models and Their Applications," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1129-1153, September.

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