论文信息 - Eine Approximation der Binomialverteilung durch die Normalverteilung der Ordnung 1/n

Eine Approximation der Binomialverteilung durch die Normalverteilung der Ordnung 1/n

SummaryThe class (1) of transformations of a binomial variablek is studied. The famous De Moivre-Laplace local and integral limit theorems are generalized for the asymptotically standardized transformations (2). The transformation (4) respectively (3) is singled out as the only one with an error of order 1/n. Besides it is shown, that the error term of ordern−1/2 of the identical transformation, the angular transformation, and the logarithmic transformation are in proportion to 1/6, −1/12, and −1/3. Results on the influence of a correction of unbiasedness are mentioned in the last section. Such corrections allow a slight improvement of our new transformation.

Rudolf Borges

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