|Life Table Forecasting with the Gompertz Distribution
|First, this paper investigates the properties of the Gompertz distribution and the relationships of their constants. Then the use of Gompertz´s law to describe mortality is discussed with male and female period life table data of the United States between 1900 and 2000. For this purpose a model incorporating time trends has been formulated with age, time and the product of age and time as independent variables and the force of mortality as the dependent variable. The parameters of the model are estimated using the least squares method. Since the mortality of modern developed population is largely the mortality of old age this generalized 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 like expectation of life, modal age, Keyfitz´entropy or old age dependency ratios. These and other parameters are forecast up to the year 2100 and compared with recent mortality forecasts of the Social Security Administration. While similar results for the male population can be observed, a greater difference between male and female mortality are forecast. Although the time dependent Gompertz model reveals systematic underestimation of mortality at young ages and overestimation at the oldest ages it is a very useful, an easy, and a quick tool for obtaining forecasts of important parameters of life tables with low mortality.
|American Statistical Association
|JSM Proceedings, Social Statistics Section. Alexandria, VA: American Statistical Association, 2007, 3564-3571
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