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<p>Examining the distributional assumptions is one of the primary steps in any data analysis. One important approach to this problem, especially in this computer age, is examination through data visualization. In this article, we revisit this classical problem in the context of normality, and multivariate normality as well as any general continuous univariate probability distribution. We take a cumulant generating function approach. We do so via <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(T_3\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation> plot of Sucharita Ghosh and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(T_4\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mn>4</mn> </msub> </math></EquationSource> </InlineEquation> plot, which we define here. These plots provide an effective and efficient visual way to examine the distributional assumptions as well as the extent of departure from them.</p>

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A Revisit to the Graphical Examination of Normality, Multinormality and Other Probability Distributions

  • 期刊论文

  • 发表日期：

    2025年8月30日

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  • Huong N. Q. Tran,
  • Ravindra Khattree

摘要

Examining the distributional assumptions is one of the primary steps in any data analysis. One important approach to this problem, especially in this computer age, is examination through data visualization. In this article, we revisit this classical problem in the context of normality, and multivariate normality as well as any general continuous univariate probability distribution. We take a cumulant generating function approach. We do so via \(T_3\) T 3 plot of Sucharita Ghosh and \(T_4\) T 4 plot, which we define here. These plots provide an effective and efficient visual way to examine the distributional assumptions as well as the extent of departure from them.