  In this survey we present an extensive research of the vast literature about
the Generalized Lambda Distribution (GLD) and propose a hurdle, or two-way,
model whose associated distribution is the GLD in order to meet the demand for
a highly flexible model of heavy-tailed data with excess of zeros. We apply the
developed models to a dataset consisting of yearly healthcare expenses, a
typical example of heavy-tailed data with excess of zeros. The fitted models
are compared with models based on the Generalised Pareto Distribution and it is
established that the GLD models perform best.
