  Variational principles for the rate distortion (RD) theory in lossy
compression are formulated within the ambit of the generalized nonextensive
statistics of Tsallis, for values of the nonextensivity parameter satisfying $
0 < q < 1 $ and $ q > 1 $. Alternating minimization numerical schemes to
evaluate the nonextensive RD function, are derived. Numerical simulations
demonstrate the efficacy of generalized statistics RD models.
