The Graduation Of Life Table And Select-and-ultimate Tables

In this dissertation, author applies a modified one-dimensional Whittaker graduation to Select-and-ultimate Tables. This modified Whittaker graduation is based on the assumption that the forces of mortality of selection of groups is under Compertze model. The effect of this modified one-dimensional method is the same as the one of two-dimensional Whittaker graduation, and therefore the method is simpler and costs much less calculation. In addition, author doubts the feasibility of wavelet graduation given by Chen Weighing.Chapter 1 is devoted to the definitions of several graduations which mainly refer to the fitting and smoothness of amendment of the initial estimate. A brief introduction to the graduation of several ways is given at the end of this Chapter. In Chapter 2, the basic methods and the framework of Life Table and the basic form of Select-and-ultimate Tables are introduced.In Chapter 3, several methods of Graduation of Life Table are introduced: M-W-A, Whittaker, Bayesian, Parameter and Spline Graduation.In Chapter 4, the infeasibility of wavelet graduation is discussed in this chapter. In Chapter 5, author firstly introduces the traditional two-dimensional Whittaker graduation on Select-and-ultimate Tables, and then gives a new method of graduation on Select-and-ultimate Tables. After that author gives a method to estimate the parameters of the functions of the force of mortality on select-and-ultimate tables based on the Compertze model. This method first uses the least square method to pre-estimate these parameters, and then applies a modified one-dimensional Whittaker graduation to them to obtain the graduation parameters. Compared with the traditional method, which first uses two-dimensional Whittaker graduation on the data of select-and-ultimate tables, and then applies the least square method to estimate the parameters the functions of the force of mortality, our method is simpler and much less calculation with the same good results. At last, an example is given to illustrate the validity of this method.