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Estimation of the mean and the initial probabilities of a branching process

Published online by Cambridge University Press:  14 July 2016

Jean-Pierre Dion
Jean-Pierre Dion*
Affiliation:
Université du Québec à Montréal
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Abstract

In this article, we consider maximum likelihood estimators of the initial probabilities and the mean of a supercritical Galton-Watson process; we find for these estimators, as well as for the Lotka-Nagaev estimator of the mean, the asymptotic distributions and deduce confidence intervals. As these results hold even if the independence between individuals of the same generation is not satisfied, application to living populations may be considered.

Keywords

GALTON-WATSON PROCESSMAXIMUM LIKELIHOOD ESTIMATORSASYMPTOTIC PROPERTIESCONFIDENCE INTERVALS
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 687 - 694
Copyright
Copyright © Applied Probability Trust 1974 

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Footnotes

This work is part of the author's doctoral dissertation done at the Université de Montréal under the guidance of Professor C. H. Kraft and with the financial support of the Department of Mathematics and the National Research Council of Canada.

References

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