Einseitige fehlerabschätzungeu im zentralen grenzwertsatz

Independent random variables with finite variances are considered,whose standardized distribution function F n of the sum of these random variables converges with increasing n to the distribution function φ of the standard normal distribution. In order to derive qualitative and quantitative erroestimates of the difference F n - φ for an arbitary fixed n onesided assumptions to the considered random variables are made additionally. On the positive real half-axis the existence of so-called onesided moments of an order greater a 2 and on the negative half-axis a sufficiently quick decrease of the tails of variances are assumed (cp. conditions (1.4) and (1.6)).In the theorems 1, 3 and 4 non-uniform onesided bounds are given. Theorem 2 contains an uniform estimate. In addition to the argument x of the distribution functions F n and φ an onesided analog to the known LJAPUNOV-fractin and an absolute constant, whose analytic structure is exact stated and illustrated in numerical examples. appear in the bounds. The article is a continuation of the researchs carried through by the author under the supposition of the existence of onesided third moments (s. [5, 6, 10]) and it generalizes known results.

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