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Semilinear credibility with several approximating functions. (English) Zbl 0571.62095

Usual credibility estimators are linear functions of the observable random variables. Semilinear credibility estimators are linear functions of some function f of the observable random variables. The estimators mainly considered in this paper are linear functions of several functions \(f_ 1,...,f_ r\) of the observable random variables.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
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References:

[1] De Vylder, F., Optimal semilinear credibility, Vereinigung Schweizerischer Versicherungsmathematiker. Mitteilungen (1976) · Zbl 0329.62077
[2] De Vylder, F.; Ballegeer, Y., A numerical illustration of optimal semilinear credibility theory, The Astin Bulletin (1979)
[3] De Vylder, F.; Goovaerts, M., The structure of the distribution of a couple of observable random variables in credibility theory, Insurance: Mathematics and Economics (1984) · Zbl 0545.62067
[4] Thyrion, P., Quelques observations statistiques sur la variable “nombre de sinistres” en assurance automobile, The Astin Bulletin (1972)
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