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On the Calculation of Variances and Credibilities by Experience Rating

Published online by Cambridge University Press:  29 August 2014

K. Loimaranta
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By experience rating the main problem is to estimate the credibilities. We have for the credibility αk the famous formula)

but it is often troublesome to find suitable estimates for the variances and . In the present paper a general method to estimate them from the actual statistics is given.

A disadvantage of the method is that good estimates require relatively extensive statistical material. If one of the variances is known, the method can be easily modified to give the other variance from statistics of moderate size.

The method is based on the Maximum Likelihood principle and leads to a system of non-linear equations. The equations can be solved by an iterative process, easily programmable for computers.

The mathematical model underlying the experience rating problem differs in our case lightly from the usual one.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 9 , Issue 1-2 , January 1977 , pp. 203 - 207
Copyright
Copyright © International Actuarial Association 1977

References

page 203 note * Bühlman, H.: Mathematical Methods in Risk Theory.

page 204 note * E g. Cramér, H., Mathematical Methods of Statistics.

page 206 note * Hovinen, E., On the Estimation of Means and Variances in the Case of Unequal Components, ASTIN Bulletin, Vol. VIIIGoogle Scholar, Part 3.