论文信息 - AN INEQUALITY FOR THE ASYMMETRY OF DISTRIBUTIONS AND A BERRY-ESSEEN THEOREM FOR RANDOM SUMMATION

AN INEQUALITY FOR THE ASYMMETRY OF DISTRIBUTIONS AND A BERRY-ESSEEN THEOREM FOR RANDOM SUMMATION

We consider random numbers Nn of independent, identically distributed (i.i.d.) random variablesXi and their sums ∑Nn i=1 Xi. Whereas Blum, Hanson and Rosenblatt [3] proved a central limit theorem for such sums and Landers and Rogge [8] derived the corresponding approximation order, a Berry-Esseen type result seems to be missing. Using an inequality for the asymmetry of distributions, which seems to be of its own interest, we prove, under the assumptionE|Xi| < ∞ for someδ ∈ (0, 1] andNn/n → τ (in an appropriate sense), a Berry-Esseen theorem for random summation.

N. Schmitz | Hendrik Kläver

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