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A Unified Derivation of the Complementary Waiting Time Distribution in Sequential Occupancy

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  • Charalambos A. Charalambides

    (University of Athens)

Abstract

Occupancy distributions are defined on the stochastic model of random allocation of balls to a specific number of distinguishable urns. The reduction of the joint distribution of the occupancy numbers, when a specific number of balls are allocated, to the joint conditional distribution of independent random variables given their sum, when the number of balls allocated is unspecified, is a powerful technique in the study of occupancy distributions. Consider a supply of balls randomly distributed into n distinguishable urns and assume that the number X of balls distributed into any specific urn is a random variable with probability function P(X = x) = q x , x = 0, 1,.... The probability function of the number L r of occupied urns until r balls are placed into previously occupied urns is derived in terms of convolutions of q x , x = 0, 1,... and their finite differences. Further, using this distribution, the minimum variance unbiased estimator of the parameter n, based on a suitable sequential sampling scheme, is deduced. Finally, some illustrating applications are discussed.

Suggested Citation

  • Charalambos A. Charalambides, 2006. "A Unified Derivation of the Complementary Waiting Time Distribution in Sequential Occupancy," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 345-356, September.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:3:d:10.1007_s11009-006-9750-3
    DOI: 10.1007/s11009-006-9750-3
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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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