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Mixed Cox processes, with an application to accident statistics

Published online by Cambridge University Press:  14 July 2016

M. S. Bartlett
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Abstract

A doubly stochastic switching model previously used by the author to check against doubly stochastic ‘white-noise' models is generalized in the case of Poisson processes to any distribution of fluctuating intensity rates. The resulting Cox process is used in place of a simple Poisson process as the basis of a mixed model, which is then fitted to some data on automobile accidents previously analysed by Seal (1980) in terms of a mixed Poisson process. It is shown that there is just significant evidence in favour of some additional heterogeneity ‘within' each year for individual drivers; the nature of the data analysed (yearly time intervals) does not, however, allow discrimination between heterogeneity which is definitely attributable to a common fluctuating environment, and that which is in effect independent for each driver.

Keywords

DOUBLY STOCHASTICSWITCHING MODELSMIXED MODELSAUTOMOBILE ACCIDENTSNEGATIVE BINOMIAL
Type
Part 6—Allied Stochastic Processes
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 321 - 333
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Barndorff-Nielsen, O. and Yeo, G. F. (1969) Negative binomial processes. J. Appl. Prob. 6, 633–647.Google Scholar
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Seal, H. L. (1980) Mixed Poisson processes and risk theory (Notes of a lecture course, University of Lausanne).Google Scholar