The Two-dimensional Graduation Of Select-and-ultimate Life Tables

The core of this dissertation is aboat two-dimensional graduation of select-and-ultimate life tables, and puts forward the mixed difference two-dimensional Whittaker graduation method. Compared with the traditional method, our method will make smooth metric accuracy higher and make the graduation effect better. In addition, this dissertation also discusses the parameters graduation problem of Select-and-ultimate Tables data under Weibull model,and gives rough estimates and graduation result of two parameters.This dissertation is divided into five chapters. The first chapter simply introduces Life Table and graduation content, and also describes the achievement of this dissertation; the second chapter introduces the basic framework and related Symbols of Life Table in detail,and several general methods of Graduation of Life Table are also introduced. In the third chapter, author puts forward the mixed difference two-dimensional Whittaker graduation method and gives its matrix expression as well as general expression. Compared with the traditional method, our method will make smooth metric accuracy higher because of the introduction of mixed difference operator. The graduation method is effective for general two-dimensional data as well as Select-and-ultimate Tables. The fourth chapter mainly discusses the parameters graduation problem of Select-and-ultimate Tables data under Weibull model. Firstly the rough estimates of two parameters are given throuth the nonlinear least square method,and then author deduces the parameters graduation results by way of a modified one-dimensional Whittaker graduation method. The calculation and graduation process are both improved. The example indicates the validity of this method.