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

The Burr 12 Distribution Family and the Maximum Entropy Principle: Power-Law Phenomena are not necessarily Nonextensive