Advertisement

Bulletin of Mathematical Biology

, Volume 36, Issue 4, pp 445–454 | Cite as

On the probability of reaching a threshold in a stochastic mammillary system

  • J. H. Matis
  • M. Cardenas
  • R. L. Kodell
Article

Abstract

The multivariate distribution over time of a particular stochastic mammillary compartmental model is obtained for any point in time. The maximum expectation of the peripheral compartments is then derived and used to determine lower bounds on the probability that the maximum of the peripheral compartments reaches any arbitrary threshold level. A bound on the probability is illustrated by an example and some of its implications are explored.

Keywords

Maximum Expectation Central Compartment Multinomial Distribution Peripheral Compartment Multivariate Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Arnason, A. N. 1972. “Parameter Estimates from Mark-Recapture Experiments on Two Populations Subject to Migration and Death.”Res. Pop. Ecology,13, 33–48.Google Scholar
  2. Feller, W. 1968.An Introduction to Probability Theory and Its Applications. New York Wiley, 3rd edn., Vol. I.Google Scholar
  3. Johnson, N. L. and S. Kotz. 1969.Discrete Distributions. Boston: Houghton Mifflin.MATHGoogle Scholar
  4. Lea, D. E. 1946.Actions of Radiations on Living Cells. Cambridge: Cambridge University Press.Google Scholar
  5. Mallows, C. L. 1968. “An Inequality Involving Multinomial Probabilities.”Biometrika,55, 422–424.MATHCrossRefGoogle Scholar
  6. Mantel, N. and W. R. Bryan. 1961. “Safety Testing of Carcinogenic Agents.”J. nat. Cancer Inst.,27, 455–470.Google Scholar
  7. Matis, J. H. and H. O. Hartley. 1971. “Stochastic Compartmental Analysis: Model and Least Squares Estimation from Time Series Data.”Biometrics,27, 77–102.CrossRefGoogle Scholar
  8. Sheppard, C. W. 1962.Basic Principles of the Tracer Method. New York: Wiley.Google Scholar
  9. Thakur, A. K., A. Rescigno and D. E. Schafer. 1973. “On the Stochastic Theory of Compartments: II. Multi-Compartment Systems.”Bull. Math. Biophysics,35, 263–271.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1974

Authors and Affiliations

  • J. H. Matis
    • 1
  • M. Cardenas
    • 1
  • R. L. Kodell
    • 1
  1. 1.Institute of StatisticsTexas A & M UniversityCollege StationUSA

Personalised recommendations