Modelling claim number using a new mixture model: negative binomial gamma distribution
Yasemin Gençtürk, Ayten Yîḡîter · Journal of Statistical Computation and Simulation · 2015
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( −λ) 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.