Small area models for skew and kurtotic variables

Models for small area estimation, used in the economic field, often have the necessity to assume or to lead back through appropriate transformations to the normality of the dependent variable. This work tries to extend the well known methodology of small area estimation at unit level with a family of models (Generalized additive model for location, scale and shape), which do not need the assumption of normality but which, as special case, has in itself most of the uni-variate models presented in literature.