# KREDIBILITAS DENGAN PENDEKATAN BÜHLMANN

NATALIA, KRISTINA (2007) KREDIBILITAS DENGAN PENDEKATAN BÜHLMANN. Other thesis, Universitas Sebelas Maret. PDF - Published Version Download (567Kb)

## Abstract

ABSTRACT Kristina Natalia, 2007.CREDIBILTY WITH BÜHLMANN APPROACH. Faculty of Mathematics and Natural Sciences. Sebelas Maret University. Credibility theory is a rate making process which allows actuary to adjust the future premiums according to the past experience. In credibility theory, there are three approaches to determine estimate credibility µ ) 1 ( Z X Z C − + = , where Z is credibility factor, X is the mean of the current observations, and µ is the prior mean. One of the approach to determine estimate credibility is greatest accuracy credibility approach by using Bühlmann model. Bühlmann defined credibility factor Z as K n n Z + = , 1 0 ≤ ≤ Z , n is the number of trial and K is Bühlmann credibility parameter. The aims of this final project are to determine estimate credibility C using Bühlmann model and to estimate parameters of Bühlmann credibility. The method used in this final project is a literary study. Based on the result, it can be concluded that to determine estimate credibility using Bühlmann credibility, involves application analysis of variance, calculation of the expected value of the process variance and calculation of the variance of the hypothetical means. Parameters of Bühlmann credibility were estimated based on empirical observation. Unbiased estimator for expected value of process variance is         − − =       = ∑∑ ∑ == = r i n t i it r i i x x n r r v 11 2 1 2 ) ( ) 1 ( 1 ˆ 1 ˆ σ and unbiased estimator for variance of the hypothetical means is . ) ( ) 1 ( 1 ) ( 1 1 ˆ 11 2 1 2 n x x n r x x r a r i n t i it r i i       −         − − −       − = ∑∑ ∑ == = Estimation for Bühlmann credibility parameter is a v K ˆ ˆ ˆ = . Therefore estimator of credibility factor is K n n Z ˆ ˆ + = , and estimator of estimate credibility is µ ˆ ) ˆ 1 ( ˆ ˆ Z x Z C i − + = , .

Item Type: Thesis (Other) Q Science > QA Mathematics Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika Saputro Bagus 13 Jul 2013 05:36 13 Jul 2013 05:36 https://eprints.uns.ac.id/id/eprint/2989