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The theory of Extreme Physical Information (EPI) is used to deduce aprobability density function (PDF) of a system that exhibits a power law tail.The computed PDF is useful to study and fit several observed distributions incomplex systems. With this new approach it is possible to describe extreme andrare events in the tail, and also the frequent events in the distribution head.Using EPI, an information functional is constructed, and minimized usingEuler-Lagrange equations. As a solution, a second order differential equationis derived. By solving this equation a family of functions is calculated. Usingthese functions it is possible to describe the system in terms of eigenstates.A dissipative term is introduced into the model, as a relevant term for thestudy of open systems. One of the main results is a mathematical relationbetween the scaling parameter of the power law observed in the tail and theshape of the head.

Theoretical model to deduce a PDF with a power law tail using Extreme Physical Information