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The structure of the distribution of a couple of observable random variables in credibility theory. (English) Zbl 0545.62067

Authors’ summary: We consider Bühlmann’s classical model in credibility theory and we assume that the set of possible values of the observable random variables \(X_ 1,X_ 2,..\). is finite, say with n elements. Then the distribution of a couple \((X_ r,X_ s)\) (\(r\neq s)\) amounts to a square real matrix of order n, that we call a credibility matrix. In order to estimate credibility matrices or to adjust roughly estimated credibility matrices, we study the set of all credibility matrices and some particular subsets of it.
Reviewer: A.Reich

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
15A99 Basic linear algebra
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References:

[1] Bühlmann, H., Mathematical Methods in Risk Theory (1970), Springer: Springer Berlin-New York · Zbl 0209.23302
[2] De Vylder, F., Optimal semilinear credibility theory, Mitt. Verein. Schweiz. Versicherungsmath., 76, 27-40 (1976) · Zbl 0329.62077
[3] De Vylder, F.; Ballegeer, Y., A numerical illustration of optimal semilinear credibility theory, ASTIN Bulletin, 10, 131-148 (1979)
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