  The importance of power-law distributions is attributed to the fact that most
of the naturally occurring phenomenon exhibit this distribution. While
exponential distributions can be derived by minimizing KL-divergence w.r.t some
moment constraints, some power law distributions can be derived by minimizing
some generalizations of KL-divergence (more specifically some special cases of
Csisz\'ar f-divergences). Divergence minimization is very well studied in
information theoretical approaches to statistics. In this work we study
properties of minimization of Tsallis divergence, which is a special case of
Csisz\'ar f-divergence. In line with the work by Shore and Johnson (IEEE Trans.
IT, 1981), we examine the properties exhibited by these minimization methods
including the Pythagorean property.
