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.

partial sums, penultimade, stable distribution
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