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Recurrence formula and the maximum likelihood estimation of the age in a simple branching process

Published online by Cambridge University Press:  14 July 2016

M. Adès ,
J.-P. Dion ,
G. Labelle  and
K. Nanthi
M. Adès*
Affiliation:
Université du Québec à Montréal
J.-P. Dion*
Affiliation:
Université du Québec à Montréal
G. Labelle*
Affiliation:
Université du Québec à Montréal
K. Nanthi*
Affiliation:
Presidency College, Madras
*
∗ Postal address: Université du Québec àMontréal, Case Postale 8888, Succ. A, Montréal, P.Q. H3C 3P8, Canada.
∗ Postal address: Université du Québec àMontréal, Case Postale 8888, Succ. A, Montréal, P.Q. H3C 3P8, Canada.
∗ Postal address: Université du Québec àMontréal, Case Postale 8888, Succ. A, Montréal, P.Q. H3C 3P8, Canada.
∗∗ Postal address: Presidency College, Madras-5, India.
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Abstract

In this paper, we consider a Bienaymé– Galton–Watson process {Xn ; n ≧ 0; Xn = 1} and develop a recurrence formula for P(Xn = k), k = 1, 2, ···. The problem of obtaining the maximum likelihood estimate of the age of the process when p 0 = 0 is discussed. Furthermore the maximum likelihood estimate of the age of the process when the offspring distribution is negative binomial (p 0 ≠ 0) is obtained, and a comparison with Stigler's estimator (1970) of the age of the process is made.

Keywords

BRANCHING PROCESSMAXIMUM LIKELIHOOD ESTIMATIONSTIGLER'S ESTIMATORRECURRENCE FORMULA
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 776 - 784
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

This research was supported by grants FCAC 504, NSERC A 8852 and FCAC 1608.

References

Ades, M., Dion, J. P. and Labelle, G. (1981) On estimating the age of a supercritical branching process. Technical Report, Université du Québec à Montréal.Google Scholar
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