Fitting the Erlang mixture model to data via a GEM-CMM algorithm

Abstract

The Erlang mixture model with common scale parameter is flexible and analytically tractable. As such, it is a useful model to fit insurance loss data and to calculate quantities of interest for insurance risk management. In this paper, we propose a generalized expectation–maximization (GEM) algorithm along with a clusterized method of moments (CMM) to estimate the model parameters. The GEM algorithm not only estimates the mixing weights and scale parameter of the model but also estimates the shape parameters of the model using a local search method. The CMM method enables to produce quality initial estimates for the GEM algorithm. As a result, the proposed approach provides an efficient algorithm that can fit the model to the body and the tail of truncated and censored loss data well and converges fast. We examine the performance of the proposed approach through several simulation studies and apply it to fit the Erlang mixture model to two real loss data sets.