NONLINEAR IMPLICIT REGRESSION FIT OF THE MORTALITY DATA BY THE THREE PARAMETER GENERALIZED LOGISTIC MODEL

Abstract

In this work, a generalized logistic model involving three parameters is proposed for the population mortality data fitting. The analytic solution of this new model is derived in terms of the hypergeometric function which is difficult to apply to the formulation for optimal parameters to automate the least square fit of the data. To overcome this difficulty, the differential equation model is approximated by using terms in the Taylor expansion about the normalized population, resulting in a more manageable analytic solution to the modified differential equation. However, even this approximate solution is a polynomial of non-integer exponents. A nonlinear implicit least square error function is formulated with this analytic approximate solution. To illustrate the model’s effectiveness compared to the classical model, a Chinese population data set is chosen and the new model is implemented numerically to fit the data sets. It is shown that even with just two or three terms in the power series expansion, our model provides favorable fits of the data. Data is collected for the Chinese population. The results demonstrate the potential applications of our novel model for population dynamical data fitting, with a more diverse fitting data range and data type. This model can be useful in actuarial science for insurance contingency as a mortality model or a hazard function for ensuring standards in scientific and engineering processes. The goodness of fit of this model will be analyzed in the future.