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I have sets of data with a bimodal distribution and the best estimate of splitting the two seems to use the single (unique) values that can be taken, and calculate the mean. This mean value nicely separates my data, but I would like to know if this approach/function has a name (similar to mode and median).

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    $\begingroup$ Do you mean using $(u + v)/2$ where your modes are $u$ and $v$? $\endgroup$ – Nick Cox Aug 5 '19 at 23:29
  • $\begingroup$ That might be a better estimate. From reading a bit more it seems the antimode would be the best, but determining these values from a bimodal distribution seems computationally quite extensive (using R's multimode). $\endgroup$ – Geo Vogler Aug 6 '19 at 0:03
  • $\begingroup$ Distinct is a better word than unique for what I think you mean. The point is argued at length within stata-journal.com/sjpdf.html?articlenum=dm0042 $\endgroup$ – Nick Cox Aug 6 '19 at 6:04
  • $\begingroup$ Aye, agreed. I got this term because I used the ‘unique()’ function in R, but it did not feel right. Now I know that there is also a distinct() function (giving the same results). Thanks for pointing out this difference! $\endgroup$ – Geo Vogler Aug 6 '19 at 6:21
  • $\begingroup$ The same small issue arises in Stata, with overlapping unique and distinct commands, and may well do so elsewhere. My not mentioning yet other software is a matter of ignorance rather than prejudice. $\endgroup$ – Nick Cox Aug 6 '19 at 6:27
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Is it appropriate to use the mean of the unique values from a bimodal distribution to split the data?

This would not be suitable in general; in some cases the mean may lie very close to one of the modes or even outside the interval between the two modes.

bimodal distribution with right skew components where the mean is to the right of both modes

In the above histogram the vertical line marks the sample mean; as you see it's to the right of the right-most mode.

I would like to know if this approach/function has a name

Well, I'd call it mean-splitting (at least I would without doing unique() first). It wouldn't be a common thing to do for this purpose.

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