  A general characterization for \alpha-unimodal distributions was provided by
Alamatsaz (1985) who later introduced a multivariate extension of them
(Alamatsaz 1993). Here, by solving the related equations, another
generalization for unimodality is presented. As a result of this
generalization, a simpler proof of a conjecture, as well as a characterization
for generalized arcsin distributions and some generalizations of the author's
earlier works, have been obtained. Last, but not the least, it is shown that
some elementary methods can be more powerful than some more advanced
techniques.
