On the theory of mortality measurement

Abstract

Abstract When the mortality structure of an insurance collective is estimated from empirical data, the deviation between the true and estimated mortality is caused by various factors which can be grouped in the following way: 1. (i) Sampling errors. In general the data available have not been obtained by a randomized procedure according to the rules of sampling theory. Clearly the various forms of selection that are present will introduce some bias in the mortality measurements. Further, the sampling population may not be sufficiently well defined (e.g. choice of sampling unit: person, insurance policy or risk sum) or it maybe too heterogeneous to allow the relevant inferences to be made. To achieve a certain degree of homogeneity stratification may be applied as is usually done with respect to age, sex and possibly other variables.2. (ii) Prediction errors. The mortality estimates will be used to compute premiums, reserves and so on. Strictly speaking it is the future mortality that is of interest here, and we will then have to make a prognosis, often for several decades forward in time. As the development of the mortality depends upon factors that are very difficult to handle, it is likely that only a rough prognosis can be made. The mortality will be influenced by medical progress, changes in the social structure, economic fluctuations and other variables that are difficult to predict.3. (iii) Random fluctuations due to the finite sample-size. In demographic studies the sample-size is often very large (sometimes even complete enumeration) while in actuarial mortality investigations the available material may be of moderate size. Hence in the latter case one has to pay more attention to this sort of error. Even smaller samples are sometimes met with in certain biometric mortality studies.4. (iv) Many different methods of estimation are in current usage for measuring mortality. The efficiency of a method may be expressed by its mean square error, and one wants naturally an estimate of high efficiency. At the same time it should be simple to apply in practice without too cumbersome computations.