Large Deviations Principle for Occupancy Problems with Colored Balls
- 1 March 2007
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 44 (1), 115-141
- https://doi.org/10.1239/jap/1175267167
Abstract
A large deviations principle (LDP), demonstrated for occupancy problems with indistinguishable balls, is generalized to the case in which balls are distinguished by a finite number of colors. The colors of the balls are chosen independently from the occupancy process itself. There arerballs thrown intonurns with the probability of a ball entering a given urn being 1/n(i.e. Maxwell-Boltzmann statistics). The LDP applies with the scale parameter,n, tending to infinity andrincreasing proportionally. The LDP holds under mild restrictions, the key one being that the coloring process by itself satisfies an LDP. This includes the important special cases of deterministic coloring patterns and colors chosen with fixed probabilities independently for each ball.Keywords
This publication has 13 references indexed in Scilit:
- Large deviation asymptotics for occupancy problemsThe Annals of Probability, 2004
- Bins and balls; Large deviations of the empirical occupancy processThe Annals of Applied Probability, 2002
- Optical switch dimensioning and the classical occupancy problemInternational Journal of Communication Systems, 2002
- An overview of closed capture-recapture modelsJournal of Agricultural, Biological and Environmental Statistics, 2001
- Large deviations at equilibrium for a large star-shaped loss networkThe Annals of Applied Probability, 2000
- Confidence intervals for the number of unseen typesStatistics & Probability Letters, 1998
- Assessing software designs using capture-recapture methodsIEEE Transactions on Software Engineering, 1993
- Large Deviations for Markov Processes with Discontinuous Statistics, I: General Upper BoundsThe Annals of Probability, 1991
- Blocking When Service Is Required From Several Facilities SimultaneouslyAT&T Technical Journal, 1985
- ON ESTIMATING THE SIZE OF MOBILE POPULATIONS FROM RECAPTURE DATABiometrika, 1951