Ardiani, Nila (2007) Penentuan distribusi Claim Aggregate berdasarkan distribusi jumlah Claim. Sarjana thesis, Universitas Brawijaya.
Abstract
Claim aggregate merupakan total claim yang terjadi pada suatu perusahaan asuransi dalam jangka waktu tertentu dinotasikan S . Untuk memperoleh fungsi distribusi kumulatif dari S , diketahui lebih dahulu berapa banyak claim yang terjadi dan dengan hukum total peluang diperoleh * 0 ( ) ( )Pr( n ) S n F x P x N n ∞ = =Σ = , dimana N adalah jumlah claim yang dihasilkan oleh polis pada portofolio untuk periode waktu tertentu dan x adalah jumlah claim dari masing-masing individu. Jika jumlah claim ( N ) berdistribusi Poisson, maka claim aggregatenya berdistribusi compound Poisson dengan 1 E [ S ]= λ p , 2 Var [ S ]= λ p dan ( ) [ Mx ( t ) 1] S M t = e λ − .Sedangkan jika jumlah claim ( N )digunakan distribusi binomial negatif, maka distribusi claim aggregatenya disebut distribusi compound binomial negatif, dengan 1 E [ S ] p rq p = , 2 2 2 2 1 Var [ S ] rq p rq p p p = + dan ( ) 1 () r S X M t p qM t = − .
English Abstract
Claim aggregate represent totally of claim that happened at one particular company of certain insurance within notation S . To derive the distribution function of S , distinguished according to how many claims occur and use the law of total probability, * 0 ( ) ( )Pr( n ) S n F x P x N n ∞ = =Σ = . where N denote the number of claims produced by a portofolio of policies in a given time period and x denote the amount of claim from each individual. If the number of claims ( N ) has Poisson distribution, the distribution of aggregate claims is called a compound Poisson distribution with 1 E [ S ]= λ p , 2 Var [ S ]= λ p and ( ) [ Mx ( t ) 1] S M t = e λ − . When a negative binomial distribution is choosen for the number of claim ( N )the distribution of aggregate claims is called a compound negative binomial, with 1 E [ S ] p rq p = , 2 2 2 2 1 Var [ S ] rq p rq p p p = + and ( ) 1 () r S X M t p qM t = − .
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2007/217/050703249 |
| Subjects: | 500 Natural sciences and mathematics > 510 Mathematics |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Unnamed user with email repository.ub@ub.ac.id |
| Date Deposited: | 13 Dec 2007 09:32 |
| Last Modified: | 07 Mar 2022 03:39 |
| URI: | http://repository.ub.ac.id/id/eprint/151718 |
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