  In actuarial practice the dependency between contract limitations
(deductibles, copayments) and health care expenditures are measured by the
application of the Monte Carlo simulation technique. We propose, for the same
goal, an alternative approach based on Generalized Linear Model for Location,
Scale and Shape (GAMLSS). We focus on the estimate of the ratio between the
one-year reimbursement amount (after the effect of limitations) and the one
year expenditure (before the effect of limitations). We suggest a regressive
model to investigate the relation between this response variable and a set of
covariates, such as limitations and other rating factors related to health
risk. In this way a dependency structure between reimbursement and limitations
is provided. The density function of the ratio is a mixture distribution,
indeed it can continuously assume values mass at 0 and 1, in addition to the
probability density within (0, 1) . This random variable does not belong to the
exponential family, then an ordinary Generalized Linear Model is not suitable.
GAMLSS introduces a probability structure compliant with the density of the
response variable, in particular zero-one inflated beta density is assumed. The
latter is a mixture between a Bernoulli distribution and a Beta distribution.
