  In a comparative study, the q-exponential and Weibull distributions are
employed to investigate frequency distributions of basketball baskets, cyclone
victims, brand-name drugs by retail sales, and highway length. In order to
analyze the intermediate cases, a distribution, the q-Weibull one, which
interpolates the q-exponential and Weibull ones, is introduced. It is verified
that the basketball baskets distribution is well described by a q-exponential,
whereas the cyclone victims and brand-name drugs by retail sales ones are
better adjusted by a Weibull distribution. On the other hand, for highway
length the q-exponential and Weibull distributions do not give satisfactory
adjustment, being necessary to employ the q-Weibull distribution. Furthermore,
the introduction of this interpolating distribution gives an illumination from
the point of view of the stretched exponential against inverse power law
(q-exponential with q > 1) controversy.
