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Marginal-sum and maximum-likelihood estimation in a multiplicative tariff

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Abstract

It is well known that, for a multiplicative tariff with independent Poisson distributed claim numbers in the different tariff cells, the maximum-likelihood estimators of the parameters satisfy the marginal-sum equations. In the present paper we show that this is also true under the more general assumption that the claim numbers of the different cells arise from the decomposition of a collective model for the whole portfolio of risks. In this general setting, the claim numbers of the different cells need not be independent and need not be Poisson distributed.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Rostock, 18051, Rostock, Germany

    Klaus T. Hess

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  1. Klaus T. Hess
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Correspondence to Klaus T. Hess.

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Hess, K.T. Marginal-sum and maximum-likelihood estimation in a multiplicative tariff. AStA Adv Stat Anal 93, 221–233 (2009). https://doi.org/10.1007/s10182-008-0079-9

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  • DOI: https://doi.org/10.1007/s10182-008-0079-9

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