Abstract
We use a variety of real inversion formulas to derive the structure distribution in a mixed Poisson process. These approaches should prove to be useful in applications, e.g., in insurance where such processes are very popular.This article is dedicated to the memory of Roland L. Dobrushin.
Highlights
One of the most classical examples of a counting process {N(t);t >_ O} is the homogeneousPoisson process
Even when the number of claims for each individual policy follows a Poisson distribution, the averages vary over the portfolio
This means that the value A for an individual policy is one of the possible values of a random variable A
Summary
One of the most classical examples of a counting process {N(t);t >_ O} is the homogeneous. Even when the number of claims for each individual policy follows a Poisson distribution, the averages vary over the portfolio This means that the value A for an individual policy is one of the possible values of a random variable A. Albrecht [3] studied estimators for the case of a mixture of a known finite number of Poisson components In all these estimators, one uses the number of claims in successive repetitions of the process. An alternative approach is due to Karr [10], who estimated H by inverting the Laplace transform In this case, only the time epoch of the first claim in each of the realizations of the MPP is used. Our approach is more in the spirit of Karr’s
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