Dealing with limitations of empirical mortality data in small populations

It is fairly well established that empirical age-specific mortality data are often characterized by a number of limitations and deficiencies the most common of which is a pronounced tendency in age declaration to “round-off” to certain preferred digits. Another typical limitation of such data is that in many times they are only available aggregated in five-year age groups and/or they are incomplete. In addition to these problems, special limitations related to the efficiency and stability of the empirical death data also arise when these data refer to small populations. In such cases, the age-specific death rates are inefficient estimators of the corresponding death probabilities as a result of the highest impact of randomness. However, for many purposes in both demographic analysis and actuarial practice, there is a need for both reliable and analytical estimation of age-specific mortality patterns. This article provides a review of the typical problems and limitations affecting mortality data of small populations, discusses their consequences in estimating age-specific mortality patterns, and also proposes ways to deal with them. In that, a theoretically consistent though computationally simplest technique for minimizing random variations in age-specific death counts is proposed and demonstrated using empirical death counts of some chosen small populations.