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We show that the stochastic interpretation of Tsallis' thermostatistics givenrecently by Beck [Phys. Rev. Lett {\bf 87}, 180601 (2001)] leads naturally to amulti-parameter generalization. The resulting class of distributions is able tofit experimental results which cannot be reproduced within the Boltzmann's orTsallis' formalism.Comment: ReVTex 4.0, 4 eps figure

Multiparameter generalization of nonextensive statistical mechanics