Modifikasi Metode Interpolasi Kostaki dalam Menduga Tabel Hayat Lengkap Berdasarkan Tabel Hayat Ringkas

Abstract

Information about a person's chances of survival according to age is needed to predict the amount of claims to be paid by an insurance company in the future. This requires a complete life table. Several methods are available to estimate a complete life table, among others there are Elandt-Johnson, Brass Logit, Heligman-Pollard, and Kostaki methods. The purpose of this paper is to modify the Kostaki method, which then will be compared to the other interpolation methods. This method does not require a standard data in making estimation of a complete life table. Standard data are replaced by results of interpolated probability of dying on the abridged life table. The method of interpolation is a six-point Lagrangian interpolation and Heligman-Pollard (HP) method. This paper provides two alternative models of HP method. Each model has been simplified to make it easier to estimate the values of its parameters. The data are derived from the USA life tables of 2002 and 2007, which are obtained from the Human Mortality Database. The complete USA life table of 2002 is used as the standard data. The first step is to examine each of the interpolation method of abridged life table. Furthermore, a complete USA life table of 2007 is developed based on USA abridged life table 2007 using each of the methods. The last step is comparing the results obtained by each method with the empirical complete USA life table of 2007. Mean absolute error and coefficient of determination are used to test the suitability of the empirical data with the estimated data based on the methods. The results of this research recommend three best interpolation methods, namely Kostaki, modified Kostaki with Lagrangian interpolation, and Elandt-Johnson methods. Among these methods, only Kostaki method requires standard data of complete life table. Therefore, Elandt-Johnson method and modified Kostaki are recommended to be used. Between these methods, Elandt-Johnson is the most recommended, because it is simpler to apply.