We consider a set of risks B, which is divided into subsets Bi according to some property as profession, region etc. The subsets Bi are thought to be too small to permit a calculation of a premium from their own experience. On the other hand we assume that there are differences between the Bi. This paper tries to give a solution to the problem how the experience of the single Bi should be combined with that of the whole B.

The problem is treated only with respect to frequencies of claims. The amounts of the claims are not taken into consideration. I suppose that an extension of the theory to amounts is possible and highly desirable for practical applications. Lack of time did not permit me however to proceed to such an extension in this paper.

I think that the methods developed in the sequel might be applied to the following practical problems:

— rate making

— experience rating in the restrictive sense of the word, i.e. adjusting periodically the premium or granting premium refunds according to the experience of every single Bi

— judging the experience of a. Bi.

I do not give a list of references which would have to be very long. The basic idea was, as far as I know, first developed by Lundberg.