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A multinomial model for transition probability matrices

Published online by Cambridge University Press:  14 July 2016

G. G. S. Pegram
G. G. S. Pegram*
Affiliation:
University of Natal
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Abstract

A model for the transition probability matrices (t.p.m.'s) of finite discrete Markov chains is suggested which may help those who wish to use a larger number of states than would seem reasonable with the data available in the current estimation situation. The model is especially useful in that a finite t.p.m. of arbitrary size can be specified by as few as two parameters. An example of the model's estimation and use is presented, showing it in a fair light in comparison with the conventional method of t.p.m. specification.

Keywords

FINITE DISCRETE MARKOV CHAINSAPPROXIMATIONMODELLINGBIVARIATE DISCRETE DISTRIBUTIONSPARSIMONY
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 498 - 506
Copyright
Copyright © Applied Probability Trust 1975 

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References

Anderson, T. W. and Goodman, L. A. (1957) Statistical inference about Markov chains. Ann. Math. Statist. 28, 89–110.Google Scholar
Gani, J. (1966) Flooding models. Proc. 1965 Reservoir Yield Symposium, Oxford, Part I, 4.1–4.16.Google Scholar
Lloyd, E. H. (1953) The direct product of matrices. Math. Gazette 37, 29–33.Google Scholar
Lloyd, E. H. (1963) Reservoirs with serially correlated inflows. Technometrics 5, 85–93.Google Scholar
Wishart, J. (1949) Cumulants of multivariate multinomial distributions. Biometrika 36, 47–58.Google Scholar