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I sample $n$ dimension vectors (each sample is a vector). My objective is the detection of outliers. In case those elements would distribute normally, for outlier detection, I could use Standardized Euclidean Distance, followed by extraction of the survival function based on the $\chi^2_{n}$ distribution. Unfortunately, the elements in my vector distribute with respect to $\chi^2$. What tool I should use?

Remark: Before posting this question, I have looked into a more complicated question with different specifications.

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  • $\begingroup$ Do you sample "from" the vector of length n or is this vector the result of your sampling? What is your goal? Outlier detection? $\endgroup$
    – frank
    Commented Feb 15, 2022 at 8:38
  • $\begingroup$ my objective is outlier detection. Each sample is a vector with length equals to $n$ $\endgroup$
    – Gideon Kogan
    Commented Feb 15, 2022 at 8:47
  • $\begingroup$ Do you want to find outliers in each single vector (an outlier would be an element of the vector) or do you consider a set of vectors and an outlier would be a complete vector (an odd vector amongst all the other vectors). $\endgroup$
    – frank
    Commented Feb 15, 2022 at 8:57
  • $\begingroup$ The outlier would be a complete vector. $\endgroup$
    – Gideon Kogan
    Commented Feb 15, 2022 at 10:00
  • $\begingroup$ It is difficult to see how vectors of a fixed length (norm) could possibly have a Normal distribution or how a $\chi^2$ distribution would be relevant to them. Could you explain? Perhaps instead of "length" you mean "dimension"? $\endgroup$
    – whuber ♦
    Commented Apr 26, 2022 at 18:17

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