  In this paper we investigate the flexibility of matrix distributions for the
modeling of mortality. Starting from a simple Gompertz law, we show how the
introduction of matrix-valued parameters via inhomogeneous phase-type
distributions can lead to reasonably accurate and relatively parsimonious
models for mortality curves across the entire lifespan. A particular feature of
the proposed model framework is that it allows for a more direct interpretation
of the implied underlying aging process than some previous approaches.
Subsequently, towards applications of the approach for multi-population
mortality modeling, we introduce regression via the concept of proportional
intensities, which are more flexible than proportional hazard models, and we
show that the two classes are asymptotically equivalent. We illustrate how the
model parameters can be estimated from data by providing an adapted EM
algorithm for which the likelihood increases at each iteration. The practical
feasibility and competitiveness of the proposed approach, including the
right-censored case, are illustrated by several sets of mortality and survival
data.
