Some Refinements of Probabilistic andMoment Inequalities

The probabilistic inequality established for sums of independent random variables refines one of the estimates given in the paper by D. H. Fuk and S. V. Nagaev, [Theory Probab. Appl., 16 (1971), pp. 660--675. This inequality entails, in particular, the recent results of I. Pinelis, [Ann. Probab., 7 (1979), pp. 745--789, on estimation of constants in the Rosenthal inequality.

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