Here’s a question from Reddit:

How can I find the least frequent value (antimode) between 2 modes in a bimodal distribution?

I’m only mildly self taught in anything in statistics so please be patient with my ignorance. I’ve found so little info on a Google search for “antimode” that I thought it was a word made up by the author of a random article.

Then I found one tiny mention on the Wikipedia page for “Multimodal distribution” but no citation or details beyond that it’s the least frequent value between modes.

What data do I need in order to find this number and what is the formula?

This site had a short mention of it and in their example listed:

Mode A: 33.25836

Mode B: 71.55446

Antimode: 55.06092

But I can’t seem to reverse engineer it with just this data.

Here’s the reply I wrote:

With continuous data, there is no off-the-shelf formula to compute modes or antimodes. You have to make some modeling decisions.

One option is to use kernel density estimation KDE. Adjust the parameters until, in your judgment, the result is a good representation of the distribution, and then you can read off maxima and minima.

And here’s a notebook on Colab that shows what I mean.

If you are not familiar with KDE, here’s a great animated explanation.