Asymptotic distributions of statistics and parameter estimates for mixed Poisson processes

Mixed Poisson processes have been used as natural models for events occurring in continuous or discrete time. Our main result is the derivation of the joint asymptotic distributions of statistics, including parameter estimators, computed in different time intervals from data generated by mixed Poiss...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2007-12, Vol.137 (12), p.3990-4002
Main Authors: Savani, V., Zhigljavsky, A.
Format: Article
Language:English
Subjects:
Maximum likelihood
Mixed Poisson distribution
Mixed Poisson process
Moment estimators
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Summary:Mixed Poisson processes have been used as natural models for events occurring in continuous or discrete time. Our main result is the derivation of the joint asymptotic distributions of statistics, including parameter estimators, computed in different time intervals from data generated by mixed Poisson processes. These distributions can be used, for example, to test the hypothesis about the adequacy of the mixed Poisson process against data. We provide some simulation results and test the model on actual market research data.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2007.04.016