The compound DGL/Erlang distribution in the collective risk model

In this paper the analysis of the collective risk model assuming Erlang loss, when the claim frequency follows the discrete generalized Lindley distribu- tion, is considered. After providing some new results of this discrete model, analytical expressions for the aggregate claim size distribution in general insurance in the case that the discrete generalized Lindley distribution is assumed as the primary distribution while claim size, the secondary distri- bution, is modeled using an Erlang(r) distribution (r = 1; 2). Comparisons with the compound Poisson and compound negative binomial are developed to explain the viability of the new compound model in two examples in au- tomobile insurance.