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The structure of elementary pure birth processes

Published online by Cambridge University Press:  14 July 2016

Dietmar Pfeifer
Dietmar Pfeifer*
Affiliation:
Technical University, Aachen
*
∗Postal address: Institut für Statistik und Wirtschaftsmathematik, RWTH Aachen, Wüllnerstrasse 3, D-5100 Aachen, W. Germany.
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Abstract

A complete characterization of elementary pure birth processes is given by means of record counting processes from independent (non-identically) distributed random variables.

Keywords

PURE BIRTH PROCESSRECORD VALUESCOUNTING PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 664 - 667
Copyright
Copyright © Applied Probability Trust 1982 

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References

[1] Gergely, T. and Yezhow, I. I. (1973) On a construction of ordinary Poisson processes and their modelling. Z. Wahrscheinlichkeitsth. 27, 215–232.Google Scholar
[2] Mcshane, E. J. and Botts, T. A. (1959) Real Analysis. Van Nostrand, Princeton NJ.Google Scholar
[3] Pfeifer, D. (1982) Characterizations of exponential distributions by independent nonstationary record increments. J. Appl. Prob. 19, 127–135.CrossRefGoogle Scholar
[4] Shorrock, R. W. (1972) On record values and record times. J. Appl. Prob. 9, 316–326.Google Scholar