Experience rating in subsets of risks

We consider a set of risks B, which is divided into subsets B, according to some property as profession, region etc. The subsets B, 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 B,. This paper tries to give a solution to the problem how the experience of the single Bt 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.