  Symbolic Data Analysis works with variables for which each unit or class of
units takes a finite set of values/categories, an interval or a distribution
(an histogram, for instance). When to each observation corresponds an empirical
distribution, we have a histogram-valued variable; it reduces to the case of an
interval-valued variable if each unit takes values on only one interval with
probability equal to one. Distribution and Symmetric Distribution is a linear
regression model proposed for histogram-valued variables that may be
particularized to interval-valued variables. This model is defined for n
explicative variables and is based on the distributions considered within the
intervals. In this paper we study the special case where the Uniform
distribution is assumed in each observed interval. As in the classical case, a
goodness-of-fit measure is deduced from the model. Some illustrative examples
are presented. A simulation study allows discussing interpretations of the
behavior of the model for this variable type.
