2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219145Variational 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.31 pages, 2 figures. Minor formatting and typographical changesStatistical MechanicsInformation Theorytext