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Design problems for the pure birth process

Published online by Cambridge University Press:  01 July 2016

Gerhard Becker  and
Götz Kersting
Gerhard Becker*
Affiliation:
University of Göttingen
Götz Kersting*
Affiliation:
University of Frankfurt
*
∗Postal address: Institute of Mathematical Statistics, University of Göttingen, Lotzestr. 13, D-3400 Göttingen, W. Germany.
∗∗Postal address: Institut für Angew. Mathematik, Universität Frankfurt, Robert-Meyer-Str. 10, D-6000 Frankfurt, W. Germany.
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Abstract

Let Y(t) be a pure birth process. If a maximum likelihood estimator of the birth intensity is desired and the number n of observational points and the last observation T are given in advance, it is shown that equidistant sampling is not an optimal procedure. Properties of ‘optimal' designs and the corresponding maximum likelihood estimators are investigated and compared with equidistant and continuous sampling.

Keywords

DISCRETE SAMPLINGFISHER INFORMATIONMAXIMUM LIKELIHOOD ESTIMATOROPTIMAL DESIGN

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 2 , June 1983 , pp. 255 - 273
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

This paper is SFB 135 Study No. 7.

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