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Although the univariate kurtosis is a normalized number, I have come to understand that Mardia's multivariate kurtosis is not. Would someone be so kind to explain how I can normalize this statistic or give a formula?

Data normalization works as is answered in How to normalize data to 0-1 range?: $$z_i=\frac{x_i-\min(x)}{\max(x)-\min(x)}$$

where $x=(x_1,...,x_n)$ and $z_i$ is now your $i^{th}$ normalized data.

Amonet
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  • Our [thread on this topic](https://stats.stackexchange.com/questions/282357/mardia-skewness-and-kurtosis-for-multivariate-normal) displays formulas showing explicitly how these statistics are *standardized,* which seems to fully answer your question. The concept of "normalization" you quote is rarely even applicable or useful for this purpose, making it unclear why you bring it up in this context. – whuber Jul 08 '18 at 17:10
  • Hi @whuber. Finney and DiStefano (2006) write: "... suggests that data associated with a value of Mardia's normalized multivariate kurtosis greater than 3 could produce ...". Reference is downloadable from: https://bayanbox.ir/view/3083173369357234507/Finney-DiStefano-non-normal-and-categorical-data-in-structural-equation-modeling.pdf Do I interpret them wrong? – Amonet Jul 08 '18 at 17:28
  • The quotation is from page 273 on top of the page. – Amonet Jul 08 '18 at 17:30
  • I don't see any interpretation of anything, either in the question or your comments. – whuber Jul 08 '18 at 17:41
  • I meant that the authors (Finney and DiStefano) wrote: "... suggests that data associated with a value of Mardia's normalized multivariate kurtosis greater than 3 could produce ...". Do you think that they actually meant the standardized multivariate kurtosis? – Amonet Jul 08 '18 at 18:14
  • People often use "normalize" and "standardize" interchangeably. I'm confident those authors did not mean "normalize" in the sense quoted in your question. – whuber Jul 08 '18 at 20:05

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