The calculation of mortality-rates in the construction of life tables. A mathematical statistical study

Summary

Official life tables are frequently calculated for a period of years, rather than for an individual year, and the question arises, how annual rates are to be combined, in order to give an indication of the average mortality of the period. The author examines this problem, and uses methods based on the binomial probability distribution to suggest a solution of the ‘weighting’ problem. Taking as his starting-point the work of the Dutch statistician Van Pesch, he modifies the latter's theory so as to make it applicable to the case, where mortality rates have a secular downward trend, and reaches the conclusion that the ‘most probable values for the mortality rates are not obtained by applying the weighted mean, but by the application of a weighted mean and a correction term. The inclusion of the correction term means that, practically speaking, the results do not differ from those obtained by the application of the unweighted mean. The unweighted mean, which has the advantage of requiring less computational work, may therefore be given preference over the theoretically more accurate method.’