%0 Journal Article
%T Note on a q-modified central limit theorem
%A H. J. Hilhorst
%J Statistics
%D 2010
%I arXiv
%R 10.1088/1742-5468/2010/10/P10023
%X A q-modified version of the central limit theorem due to Umarov et al. affirms that q-Gaussians are attractors under addition and rescaling of certain classes of strongly correlated random variables. The proof of this theorem rests on a nonlinear q-modified Fourier transform. By exhibiting an invariance property we show that this Fourier transform does not have an inverse. As a consequence, the theorem falls short of achieving its stated goal.
%U http://arxiv.org/abs/1008.4259v1