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A note on a one-compartment model with clustering

  • James G. Booth (a1)

Abstract

The classical one-compartment model with no input or pure death process is shown to be a limiting case of a ‘binomial cascade' model which has the same mean and in which particles exit the compartment in binomial clusters. The transition probabilities of the binomial cascade process are derived in closed form. The model is easily modified to allow Poisson input into the compartment. Distributional results are given for this model also. In particular, it is shown that the M/M/∞ queue is a limiting case.

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Postal address: Centre for Mathematics and its Applications, ANU, GPO Box 4, Canberra, ACT 2601, Australia.

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On leave from the Department of Statistics, University of Florida, Gainesville, FL 32611, USA.

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References

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Ball, F. and Donnelly, P. (1988) A unified approach to variability in compartmental models. Biometrics 44, 685694.
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.
Feller, W. (1968) An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd edn. Wiley, New York.
Karlin, S. and Taylor, H. M. (1975) A First Course in Stochastic Processes, 2nd edn. Academic Press, New York.
Loève, M. (1963) Probability Theory, 3rd edn. Van Nostrand, Princeton, NJ.
Matis, J. H. and Hartley, H. O. (1971) Stochastic compartment analysis: model and least squares estimation from time series data. Biometrics 27, 77102.
Purdue, P. (1981) Variability in a single compartment system: a note on Barnard's model. Bull. Math. Biol. 43, 111116.
Saunders, R. (1975) Conservative processes with stochastic rates. J. Appl. Prob. 12, 447456.

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A note on a one-compartment model with clustering

  • James G. Booth (a1)

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