Abstract

The classical data representation model is too restrict when the data to be analysed are not real numbers but comprise variability. That is the case when the entities under analysis are not single elements, but groups formed e.g. based on some given common properties, and the observed variability within each group should be taken into account.
In this talk, we are interested in numerical distributional data, where units are described by histogram or interval-valued variables.
We consider parametric probabilistic models for such variables, which are based on the representation of each distribution by a location measure and inter-quantile ranges, for given quantiles (global range in the case of intervals). Multivariate Normal distributions are assumed for the whole set of indicators, considering alternative structures of the variance-covariance matrix. For all cases, maximum likelihood estimators of the corresponding parameters are derived. This framework is applied to multivariate analysis of distributional data.