In certain cases partial sums of i.i.d. random variables with finite variance are better approximated by a sequence of stable distributions with indices \\alpha_n \\to 2 than by a normal distribution. We discuss when this happens and how much the convergence rate can be improved by using penultimate approximations. Similar results are valid for other stable distributions.

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Tinbergen Institute Discussion Paper Series
Tinbergen Institute

de Haan, L.F.M, Peng, L, & Iglesias Pereira, H. (1997). Approximation by Penultimate Stable Laws (No. TI 97-100/4). Tinbergen Institute Discussion Paper Series. Retrieved from