Any discussion of mortality, fertility or migration assumptions for population projections, or of the various technical questions that arise, must be preceded by some consideration of the nature and purpose of the work that has been undertaken. It should be asked why such calculations are necessary and what is expected from the results. Fundamentally, inquiry about the future of the population arises from a natural curiosity about man's surroundings in space and in time, and this does not seem to have been damped by past failures to foresee developments; otherwise, long-range projections would by now have ceased to be made, in view of the poor prospects of success. Beyond this, however, there are to-day a variety of practical reasons for which it is deemed necessary to estimate the future numbers of persons in given areas with such accuracy as is possible.

This paper deals with some technical and statistical questions in sickness benefit insurance.

In § 1 there is a survey of the various theoretical approaches to the calculation of net premiums, and the calculation of gross premiums is discussed in §2.

Some methods of calculating rates employ two basic functions: the frequencies of new cases of sickness and the duration of sickness. The derivation of these functions from the corresponding statistical data is exemplified in § 3, which contains some results from an account of the experience of a Swedish sickness insurance company. Finally, § 4 deals with some mathematical formulae for graduating data of this type.

In reference(1), some large sample significance tests and confidence intervals for mortality rates were presented. These results appear to be valid for the usual type of insurance data. Also, for an ordinary mortality study, application of a test or confidence interval does not require much additional work. This paper presents a review of reference (1) along with a discussion of the concepts involved. More extensive tables of significance tests and confidence intervals are included in this paper.

To apply the results of (1), the data must be subdivided according to the first letter of the surname of the person insured. According to present practice, such information is not recorded for a mortality study. Since this recording requires little extra effort at the initial stage of an investigation, however, such information could easily be incorporated into future mortality studies.