  Recently we have demostrated that the nonextensitivity parameter q occuring
in some applications of Tsallis statistics (known also as index of the
corresponding L\'evy distribution) is, in the q>1 case, given entirely by the
fluctuations of the parameters of the usual exponential distribution. We show
here that this interpretation is valid also for the q<1 case. The parameter q
is therefore a measure of fluctuations of the parameters of the usual
exponential distribution.
