• A STUDY ON MATHEMATICAL MODELLING FOR OLDEST-OLD MORTALITY RATES

Abstract

Five mortality models: Gompertz, Makeham, Logistic, Beard and Kannisto models have been considered for this investigation. An attempt has been made to study certain mathematical properties of these above models. The first derivative of the model describes the slope of the curve or the rate of change of the dependent variable with respect to the independent variable, whereas the second derivative of the models quantifies the rate of mortality. The main objective of this paper is to select the best fit model for projection of oldest-old mortality rates at ages 80-110 based on certain mortality data for a specific period. Using the complete life table of Japan (2005 and 2010) as input, the parameters of these mortality models have been estimated using Levenberg – Marquardt iteration procedure. The estimated parameters of these models have been used for the testing the validity of the models and for the projection of mortality rates at ages 120. Matlab version 7.11.0 has been used for the estimation of the parameters. It is observed from our result that the four parameter logistic model fits oldest-old ages mortality data better than the Gompertz and three other models.