Measuring the Rectangularization of Life Tables Using the Gompertz Distribution

Abstract

The rectangularization of life tables is defined as a trend towards a more rectangular shape of the survival curve due to increased survival and concentration of deaths around the mean age at death. Since the mortality of modern developed population is largely the mortality of old age, the Gompertz model provides a good approximation of life tables in these populations and can be used to estimate and forecast many parameters of the life table and the stationary population, such as expectation of life, modal age, age dependency ratios, and indices of the rectangularization of life tables. Formulas of known rectangularization indices are developed assuming the Gompertz distribution, whereas some new indices are proposed, too. The mathematical relationships between the single indices are shown. It is demonstrated that some mentioned indices are a function of the coefficient of variation.