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Characterizations of normal distributions supporting goodness-of-fit tests based on sample skewness and sample kurtosis

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Abstract.

Two characterizations of normal distributions based on the third conditional moment and the fourth conditional moment, respectively, are given. These results theoretically support the goodness-of-fit tests for normal distributions using the sample skewness and the sample kurtosis.

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Authors and Affiliations

  1.  Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403-0221, USA (e-mail: tnguyen@bgnet.bgsu.edu), , , , , , US

    Truc T. Nguyen

  2.  US Environmental Protection Agency, Washington, DC 20460, USA (e-mail: dinh.khoan@epamail.epa.gov), , , , , , US

    Khoan T. Dinh

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  1. Truc T. Nguyen
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  2. Khoan T. Dinh
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Received July 1997

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Nguyen, T., Dinh, K. Characterizations of normal distributions supporting goodness-of-fit tests based on sample skewness and sample kurtosis. Metrika 48, 21–30 (1998). https://doi.org/10.1007/s001840050002

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  • DOI: https://doi.org/10.1007/s001840050002

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