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Decompounding: an estimation problem for Poisson random sums. (English) Zbl 1105.62309
Summary: Given a sample from a compound Poisson distribution, we consider estimation of the corresponding rate parameter and base distribution. This has applications in insurance mathematics and queueing theory. We propose a plug-in type estimator that is based on a suitable inversion of the compounding operation. Asymptotic results for this estimator are obtained via a local analysis of the decompounding functional.

MSC:
62F15 Bayesian inference
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M99 Inference from stochastic processes
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