The characteristic parameters Kw and Rw of a word w
over a finite alphabet are defined as follows: Kw is the
minimal natural number such that w has no repeated suffix of
length Kw and Rw is the minimal natural number such that
w has no right special factor of length Rw. In a previous
paper, published on this journal, we have studied the
distributions of these parameters, as well as the distribution of
the maximal length of a repetition, among the words of each length
on a given alphabet. In this paper we give the exact values of
these distributions in a special case. However, these values give
upper bounds to the distributions in the general case. Moreover,
we study the most frequent and the average values of the
characteristic parameters and of the maximal length of a
repetition over the set of all words of length n.