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) identifier identifier


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.