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Composite probability models have shown very promising results for modelingclaim severity data comprised of small, moderate, and large losses. In thispaper, we introduce three classes of parametric composite regression modelswith a varying threshold. We consider the Lognormal distribution for the headand the Burr, the Stoppa and the generalized log-Moyal (GlogM) distributionsfor the tail part of the composite family. Further, the Mode-Matching procedurehas been utilized for the composition of the two densities. To capture theheterogeneous behavior of the policyholder's characteristics, covariates areintroduced into the scale parameter of the tail distribution. Finally, theapplicability of the proposed models has been shown using a real-worldinsurance data set.

Composite Lognormal-T regression models with varying threshold and its insurance application