A unified derivation of the complementary waiting time distribution in sequential occupancy
type: Item
instance of: scholarly article
title: A unified derivation of the complementary waiting time distribution in sequential occupancy
zbMATH Open document ID: 1108.62076
published in: Methodology and Computing in Applied Probability
publication date: 2007-01-29T00:00:00Z
review text: Occupancy distributions are defined on a stochastic model of random allocations 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 is 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 \(P(X =x) =q_x\), \(x= 0,1,\dots\) 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 \(q_x\), \(x= 0, 1,\dots\) 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.
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 62L99
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 5119592
zbMATH Keywords: finite differences
zbMATH Keywords: generalized factorial coefficients
zbMATH Keywords: random occupancy model
zbMATH Keywords: sequential sampling
zbMATH Keywords: Stirling numbers
author: Charalambos A. Charalambides
MaRDI profile type: Publication
full work available at URL: s11009-006-9750-3
OpenAlex ID: W1992633871
Wikidata QID: Q111547959
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DOI: 10.1007/S11009-006-9750-3
description: scientific article; zbMATH DE number 5119592