Zusammenfassung
In diesem Beitrage sind die asymptotischen Stichprobenverteilungen der dritten und vierten Momente eines linearen stochastischen Prozesses und auch die asymptotischen Stichprobenverteilungen der Schiefe und des Exzesses der Kurtosis hergeleitet. Die Kenntnis dieser Verteilungen erlaubt für “große” Stichproben die Abweichung der Prozeßverteilung von der Normalverteilung zu prüfen, ein Problem, das in vielen Fällen der praktischen Anwendungen wichtig ist, aber mit den klassischen Testen, welche die Unabhängigkeit der Stichprobenwerte annehmen, nicht behandelt werden kann.
Die praktische Anwendung der vorgelegten Methode ist mit einigen numerischen Beispielen illustriert.
Summary
In this paper the asymptotic distributions of the third and the fourth sampling moments of a discrete-parameter linear process are derived together with the asymptotic distributions of the sampling skewness and the excess of kurtosis. The knowledge of these distributions allows us, in the case of “large” samples, to test the departure from normality, a problem which can be regarded as important in various practical applications, but which cannot be treated with the aid of classical tests based on the assumption that the sample values are independent.
Some numerical examples illustrate the applications of the proposed tests in practice.
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Lomnicki, Z.A. Tests for departure from normality in the case of linear stochastic processes. Metrika 4, 37–62 (1961). https://doi.org/10.1007/BF02613866
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DOI: https://doi.org/10.1007/BF02613866