Many studies concerning the frequency of claims by size in health insurance are not generally known). A possible explanation of this circumstance could be the fact that in most countries this line of insurance has been brought entirely within the ambit of social insurance. Also from the side of the social insurance very few investigations have been published).

In this paper we will analyse the claim experience (relating, to the calendar year 1972) of a private health insurance business. The data have been subdivided according to three levels of coverage (in increasing order of benefits these are: class III, class IIb and class IIa). The claim payments comprise nursing costs, auxiliary costs and the fees for specialist treatment in and out of the hospital.

We will use the following notations:

Si: claim amount paid for the insured i in one year,

n: number of claims,

v: number of risks (policies insured).

In many instances the premium is simply determined as a level premium. In other words each insured pays the premium p, calculated as follows:

.

Actually we make the assumption that the claims are normally distributed, the parameters of which can be estimated as follows:

which permits the calculation of the premium according to:

.