Estimation and model selection of heterogeneous mixture distributions: an ECME algorithm-based approach

Heterogeneous mixtures and spliced distributions are commonly used models for fitting skewed data, especially in loss distribution analysis. While they guarantee additional flexibility, their estimation is typically rather difficult. In this paper we develop an Expectation Conditional Maximization Either (ECME) algorithm that allows one to estimate the parameters in a completely unsupervised manner. We also propose a likelihood-ratio test for selecting between a pure lognormal and a lognormal-Pareto distribution. With respect to a recently developed profile-likelihood method, the approach has similar statistical efficiency, but is considerably faster, thus overcoming the strong computational limitations of the profile-likelihood technique. Simulation experiments and an application to vehicle insurance illustrate the effectiveness of the estimation and testing procedures. All the codes for simulating and estimating the lognormal-Pareto mixture using the methods developed in this paper are available in the LNPar R package.