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

Charalambos A. Charalambides ()
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Charalambos A. Charalambides: University of Athens

Methodology and Computing in Applied Probability, 2006, vol. 8, issue 3, 345-356

Abstract: 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.

Keywords: Finite differences; Generalized factorial coefficients; Random occupancy model; Sequential sampling; Stirling numbers; Primary 60C05; 60E05; Secondary 62F10 (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-006-9750-3

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