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A new family of point processes which are characterized by their second moment properties

Published online by Cambridge University Press:  14 July 2016

David S. Newman
David S. Newman*
Affiliation:
The Boeing Company, Washington
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Extract

The most widely used probabilistic model of a series of “events” occurring randomly in a time or space continuum is the Poisson process. It is the proper basis for statistical analysis when general information about the rate of occurrence of events is the primary purpose of an investigation, or when the assumption of independent occurrences is reasonable and valid. A unified treatment of the statistical methods for estimating parameters in stationary and non-stationary Poisson models, and tests of the Poisson assumption against various alternatives, is contained in the lucid monograph by Cox and Lewis [6].

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 338 - 358
Copyright
Copyright © Applied Probability Trust 1970 

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References

[M] Moyal, J. E. (1962) The general theory of stochastic population processes. Acta Math. 108, 1–31.CrossRefGoogle Scholar
[1] Bartlett, M. S. (1955) Stochastic Processes. Cambridge University Press.Google Scholar
[2] Bartlett, M. S. (1949) Some evolutionary stochastic processes. J. R. Statist. Soc. B 11, 211–229.Google Scholar
[3] Bartlett, M. S. and Kendall, D. G. (1951) On the use of the characteristic functional in the analysis of some stochastic processes occurring in Physisc and Biology. Proc. Camb. Phil. Soc. 47, 65–76.Google Scholar
[4] Bhabha, H. J. and Ramakrishnan, A. (1950) On the mean square deviation of the number of electrons and quanta in the cascade theory. Proc. Indian Acad. Sci. 32, 141.Google Scholar
[5] Bogoliubov, N. N. (1946) Problems of Dynamic Theory in Statistical Physics. GITTL, Moscow-Leningrad. Translated by Gora, E. K. (1962) in Studies in Statistical Mechanics. North-Holland, Amsterdam.Google Scholar
[6] Cox, D. R. and Lewis, P. A. W. (1966) The Statistical Analysis of Series of Events. Methuen, London.Google Scholar
[7] Feller, W. (1957) An Introduction to Probability Theory and its Applications. Vol. I, Second Edition. Wiley, New York.Google Scholar
[8] Kendall, D. G. (1964) Some recent work and further problems in the theory of queues. Theor. Probability Appl. 9, 3–15.Google Scholar
[9] Kendall, D. G. (1949) Stochastic processes and population growth. J. R. Statist. Soc. B 11, 230–264.Google Scholar
[10] Kuznetsov, P. I. and Stratonovich, R. L. (1956) On the mathematical theory of correlated random points. Izv. Akad. Nauk. SSSR 20, 167–178. Annotated translation by McFadden, J. A. (1964), mimeograph.Google Scholar
[11] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar