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Erscheinungsjahr: 
2021
Quellenangabe: 
[Journal:] Statistics in Transition New Series [ISSN:] 2450-0291 [Volume:] 22 [Issue:] 3 [Publisher:] Exeley [Place:] New York [Year:] 2021 [Pages:] 123-140
Verlag: 
Exeley, New York
Zusammenfassung: 
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.
Schlagwörter: 
classes of priors
posterior regret
distortion function
Bregman loss
insurance premium
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