Sains Malaysiana 40(12)(2011): 1449–1453

Methods of Expanding an Abridged Life Tables: Comparison between Two Methods

(Kaedah Mengembangkan Jadual Hayat Ringkas: Perbandingan Antara Dua Kaedah)

Rose Irnawaty Ibrahim*

Faculty of Science and Technology, Universiti Sains Islam Malaysia

Bandar Baru Nilai, 71800, Nilai, Negeri Sembilan, Malaysia

Zailan Siri

Institute of Mathematical Sciences, Faculty of Science, University of Malaya

50603 Kuala Lumpur, Malaysia

Received: 29 September 2010 / Accepted: 1 March 2011

ABSTRACT

A question of interest in the demografic and actuarial fields is the estimation of the complete sets of qx-values when the data are given in age groups. This study presents two techniques of expanding an abridged life table to a complete ones. The two expansion techniques used in the study are King’s Osculatory Interpolation and Heligman-Pollard model. This work evaluated and compared the performance of King’s Osculatory Interpolation and Heligman-Pollard model. For that purpose, empirical data sets on abridged life tables for Malaysian populations for the period of 1991, 1995 and 1999 for both gender were collected. Then each of the expanding techniques considered was applied to these abridged data sets. The complete sets of qx-values obtained from these two techniques were then used to produce the estimated abridged ones. These results were then compared with the actual values published in the abridged life tables.

Keywords: Abridged life table; complete life table; Heligman-Pollard model; King’s osculatory interpolation

ABSTRAK

Satu soalan yang diminati dalam demografik dan bidang aktuari ialah penganggaran set-set yang lengkap bagi nilai-nilai qx apabila data yang diberikan adalah dalam kumpulan umur. Kajian ini membentangkan dua teknik mengembangkan jadual hayat ringkas kepada jadual hayat penuh iaitu interpolasi Beroskulasi King dan model Heligman-Pollard. Kajian ini menyediakan beberapa penilaian dan perbandingan bagi interpolasi Beroskulasi King dan model Heligman-Pollard. Untuk tujuan tersebut, set-set data empirik bagi jadual hayat ringkas untuk populasi Malaysia bagi tempoh 1991, 1995 dan 1999 untuk kedua-dua jantina dikumpulkan. Kemudian setiap teknik pengembangan yang dipertimbangkan diguna ke atas set-set data ringkas ini. Set-set yang lengkap bagi nilai-nilai qx yang diperolehi kemudiannya diguna untuk menjana nilai-nilai anggaran dalam jadual hayat ringkas. Keputusan ini kemudiannya dibandingkan dengan nilai-nilai dalam jadual hayat ringkas sebenar yang diterbitkan.

Kata kunci: Interpolasi beroskulasi King; jadual hayat penuh; jadual hayat ringkas; model Heligman-Pollard.

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*Corresponding author; email: rose.irnawaty@usim.edu.my