{"id":839,"date":"2023-01-15T01:13:02","date_gmt":"2023-01-15T01:13:02","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=839"},"modified":"2023-01-15T01:21:08","modified_gmt":"2023-01-15T01:21:08","slug":"finding-modes-and-antimodes","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2023\/01\/15\/finding-modes-and-antimodes\/","title":{"rendered":"Finding modes and antimodes"},"content":{"rendered":"\n

Here’s a question from Reddit<\/a>:<\/p>\n\n\n\n

\n

How can I find the least frequent value (antimode) between 2 modes in a bimodal distribution?<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

What data do I need in order to find this number and what is the formula?<\/p>\n\n\n\n

This site<\/a> had a short mention of it and in their example listed:<\/p>\n\n\n\n

Mode A: 33.25836<\/p>\n\n\n\n

Mode B: 71.55446<\/p>\n\n\n\n

Antimode: 55.06092<\/p>\n\n\n\n

But I can’t seem to reverse engineer it with just this data.<\/p>\n<\/blockquote>\n\n\n\n

Here’s the reply I wrote:<\/p>\n\n\n\n

\n

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

One option is to use kernel density estimation<\/a> 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.<\/p>\n<\/blockquote>\n\n\n\n

And here’s a notebook on Colab that shows what I mean.<\/a><\/p>\n\n\n\n

If you are not familiar with KDE, here’s a great animated explanation<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

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…<\/p>\n

Read More Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-839","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"\nFinding modes and antimodes - Probably Overthinking It<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.allendowney.com\/blog\/2023\/01\/15\/finding-modes-and-antimodes\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Finding modes and antimodes - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"Here’s a question from Reddit: How can I find the least frequent value (antimode) between 2 modes in a bimodal distribution? 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