Collective Risk Model Analysis with Negative Binomial Distribution for Claim Amount and Discrete Uniform Distribution for Claim Amount

Abstract

Insurance claims are requests submitted by policyholders to obtain protection against financial losses due to a risk. Individual claims arise whenever there is a risk, while aggregate claims are the number of individual claims in a certain period. These claims are important in managing insurance company expenses, especially for calculating aggregate losses, which are the total losses borne by the company. This study aims to analyze the average and variance of the number of claims distributed Negative Binomial and the amount of claims distributed Discrete Uniform using claim payment data from PT. Jasa Raharja (Persero) Representative of Purwakarta during 2018-2020. The collective risk model is used with the help of Easyfit software to determine the best distribution. The results of the analysis show the number of claims distributed Negative Binomial with an average of 13.2 claims and a variance of 7.6 claims, while the amount of claims distributed Discrete Uniform with an average of IDR2,108,950,000 and a variance of IDR567,850,000. The average aggregate claim is IDR 27,800,000,000 with a variance of IDR 6,270,000,000 during the period. The conclusion of this study confirms the effectiveness of the collective risk model in modeling aggregate claims for insurance data.