Sains Malaysiana 33(2): 173-194 (2004)                                                                      Pengajian Kuantitatif /

Quantitative Studies

 

Model Bilangan Tuntutan Insurans dengan Taburan

Tunggal dan Campuran Terhingga

(A Model for Insurance Claim Count With Single and

Finite Mixture Distribution)

 

 

Noriszura Hj. Ismail, Khairul Anuar Mohd Ali & Chiew Ai Chin

Pusat Pengajian Sains Matematik

Fakulti Sains dan Teknologi

Universiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor D.E., Malaysia

 

 

 

ABSTRAK

 

Kajian ini bertujuan untuk menyuai taburan diskrit terhadap data bilangan tuntutan insurans. Penyuaian yang dilakukan melibatkan taburan tunggal dan campuran terhingga. Data yang diguna merupakan data bilangan tuntutan bagi produk insurans hayat yang dikeluarkan oleh salah sebuah syarikat insurans yang terdapat di Malaysia. Data ini bertempoh 12 bulan, bermula daripada Januari 2000 sehingga Disember 2000. Kaedah momen dan kebolehjadian maksimum diguna untuk menganggar parameter bagi kedua-dua taburan tunggal dan campuran terhingga. Kebagusan suaian model diuji dengan ujian khi-kuasa dua Pearson, ujian nisbah kebolehjadian dan kriteria Bayesian-Schwartz. Hasil kajian menunjukkan bahawa model campuran terhingga memberikan penyuaian yang lebih baik berbanding dengan model tunggal. Selain itu, hasil kajian juga menunjukkan bahawa taburan campuran terhingga dua-Poisson adalah model yang terbaik bagi data.

 

 

ABSTRACT

 

This research aims to fit discrete distributions on insurance claim count data. The fitting includes both single and finite mixture distributions. The data used is claim count data for life insurance products produced by one of the insurance companies in Malaysia. The claims were paid from January 2000 until December 2000, involving a period of 12 months. The method of moments and maximum likelihood procedure are used to estimate the parameters of both single and finite mixture distributions. The Pearson chi­square test, likelihood ratio test, and Bayesian Schwartz criteria are used to test the models. The results showed that finite mixture distribution is superior to single distribution. Furthermore, the results also showed that two-Poisson finite mixture distribution is the best model for the data.

 

 

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