  In this paper we recall for physicists how it is possible, using the
principle of maximization of the Boltzmann-Shannon entropy, to derive the
Burr-Bingh-Maddala (burr12) double power law probability distribution function
and its approximations (Pareto, loglogistic ..) and extension first used in
econometrics. this is possible using a deformation of the power function, as
this has been done in complex systems for the exponential function. We give to
that distribution a deep stochastic interpretation using the theory of Weron et
al. applied to thermodynamics the entropy nonextensivity can be accounted for
by assuming that the asymptotic exponents are scale dependent. Therefore
functions which describe phenomena presenting power-law asymptotic behaviour
can be obtained without introducing exotic forms of the entropy.
