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Estimating Sample Skewness from Sample Data Summaries and Associated Evaluation of Normality

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Abstract

We propose a method to estimate a sample skewness from the given summary statistics and give explicit formulas for the most common scenarios. We show that our method provides a nearly unbiased estimator for the non-parametric skewness measure. We empirically evaluate the performance on real-life data sets of COVID-19 vaccination status. We also demonstrate how the method can be applied to detect the skewness of the underlying distribution.

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Funding

The research of the first author was funded by the Natural Sciences and Engineering Research Council of Canada RGPIN-2020-06733. The funding agency had no input in study design, analysis and interpretation of data, in the writing of the report, nor in the decision to submit the article for publication.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada

    Narayanaswamy Balakrishnan

  2. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, VA 23284, Richmond, USA

    Jan Rychtář & Dewey Taylor

Authors
  1. Narayanaswamy Balakrishnan
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  2. Jan Rychtář
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  3. Dewey Taylor
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Contributions

Narayanaswamy Balakrishnan: conceptualization, formal analysis, investigation, methodology, funding acquisition, writing—original draft, writing—review and editing. Jan Rychtář: formal analysis, investigation, methodology, software, visualization, writing—original draft, writing—review and editing. Dewey Taylor: formal analysis, investigation, methodology, software, visualization, writing—original draft, writing—review and editing.

Corresponding authors

Correspondence to Narayanaswamy Balakrishnan, Jan Rychtář or Dewey Taylor.

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Balakrishnan, N., Rychtář, J. & Taylor, D. Estimating Sample Skewness from Sample Data Summaries and Associated Evaluation of Normality. Math. Meth. Stat. 32, 260–273 (2023). https://doi.org/10.3103/S106653072304004X

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  • DOI: https://doi.org/10.3103/S106653072304004X

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