Modelling claim number using a new mixture model: negative binomial gamma distribution
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, vol.86, no.10, pp.1829-1839, 2016 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 86 Issue: 10
- Publication Date: 2016
- Doi Number: 10.1080/00949655.2015.1085987
- Journal Name: JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.1829-1839
- Hacettepe University Affiliated: Yes
Abstract
In actuarial applications, mixed Poisson distributions are widely used for modelling claim counts as observed data on the number of claims often exhibit a variance noticeably exceeding the mean. In this study, a new claim number distribution is obtained by mixing negative binomial parameter p which is reparameterized as p = exp( -lambda) with Gamma distribution. Basic properties of this new distribution are given. Maximum likelihood estimators of the parameters are calculated using the Newton-Raphson and genetic algorithm (GA). We compared the performance of these methods in terms of efficiency by simulation. A numerical example is provided.