  Composite probability models have shown very promising results for modeling
claim severity data comprised of small, moderate, and large losses. In this
paper, we introduce three classes of parametric composite regression models
with a varying threshold. We consider the Lognormal distribution for the head
and the Burr, the Stoppa and the generalized log-Moyal (GlogM) distributions
for the tail part of the composite family. Further, the Mode-Matching procedure
has been utilized for the composition of the two densities. To capture the
heterogeneous behavior of the policyholder's characteristics, covariates are
introduced into the scale parameter of the tail distribution. Finally, the
applicability of the proposed models has been shown using a real-world
insurance data set.
