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March, 1975 Maximum Likelihood Estimation in the Birth-and-Death Process
Niels Keiding
Ann. Statist. 3(2): 363-372 (March, 1975). DOI: 10.1214/aos/1176343062

Abstract

Maximum likelihood estimation of the parameters $\lambda$ and $\mu$ of a simple (linear) birth-and-death process observed continuously over a fixed time interval is studied. Asymptotic distributions for large initial populations and for large periods of observation are derived and some nonstandard results appear. The result problem of estimation from the discrete skeleton of the process is also discussed.

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Niels Keiding. "Maximum Likelihood Estimation in the Birth-and-Death Process." Ann. Statist. 3 (2) 363 - 372, March, 1975. https://doi.org/10.1214/aos/1176343062

Information

Published: March, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0302.62043
MathSciNet: MR362773
Digital Object Identifier: 10.1214/aos/1176343062

Subjects:
Primary: 62F10
Secondary: 60F05 , 60J80 , 62B05 , 62M05

Keywords: Birth-and-death process , discrete skeleton of Markov process , estimation in Markov processes , maximum likelihood estimation , weak convergence under random change of time

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 2 • March, 1975
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