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Citation Information : Statistics in Transition New Series. Volume 22, Issue 3, Pages 123-140, DOI: https://doi.org/10.21307/stattrans-2021-030
License : (CC BY-NC-ND 4.0)
Received Date : 18-September-2020 / Accepted: 09-April-2021 / Published Online: 05-September-2021
The article presents a collective risk model for the insurance claims. The objective is to estimate a premium, which is defined as a functional specified up to unknown parameters. For this purpose, the Bayesian methodology, which combines the prior knowledge about certain unknown parameters with the knowledge in the form of a random sample, has been adopted. The generalised Bregman loss function is considered. In effect, the results can be applied to numerous loss functions, including the square-error, LINEX, weighted squareerror, Brown, entropy loss. Some uncertainty about a prior is assumed by a distorted band class of priors. The range of collective and Bayes premiums is calculated and posterior regret Γ-minimax premium as a robust procedure has been implemented. Two examples are provided to illustrate the issues considered - the first one with an unknown parameter of the Poisson distribution, and the second one with unknown parameters of distributions of the number and severity of claims.
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