# Why is $\pi$ used in logistic regression?

Why is $\pi$ used to denote probability in logistic regression?

Rather than something that does not create confusion with the more common use of $\pi$ as the circumference of a circle or the specific number $3.14 ...$?

Does using $\pi$ in logistic regression pertain some special meaning (like the more known $\pi=3.14...$) or is it just a symbol that has been chosen?

It seems to be pretty widely used:
http://www.google.com/search?q=logistic+regression+pi

• Authors are free to use whatever notation they like, aren't they? Did you come across this particular notation in a paper, or maybe some notes? – Adrian Sep 28 '16 at 12:12
• No $\pi$ on, e.g., German or English Wikipedia. And not so sure lmgtfy is appropriate when someone gives a comment on your question. – Christoph Hanck Sep 28 '16 at 12:23
• If I had to guess, I'd say it's because $\pi$ is related to the roman letter $p$, which is the first letter in "probability". See web.mit.edu/jmorzins/www/greek-alphabet.html. – Adrian Sep 28 '16 at 13:22
• $\pi$ used to be pretty standard for the population probability in the binomial, following the usual convention of Greek letters for parameters ($\mu$ for mean, $\sigma$ for standard deviation,$\pi$ for probabiiity, and so on). It's less common now (you see $p$ used a lot more). Logistic regression is a model for a binomial proportion, so it's little surprise that it followed suit and sometimes also used $\pi$ to represent that binomial proportion it models. – Glen_b Sep 28 '16 at 14:41
• It might be how the question was formulated that the community finds less than useful. It implicitly assumes some kind of context--a paper, a book, some other written account--that has not been mentioned or quoted, but which nevertheless is crucial to understanding and answering the question. – whuber Sep 28 '16 at 16:20

## 1 Answer

Because $\pi$ is the standard symbol for the unknown population value following the usual convention of using Greek letters and reserving the Roman for sample values.