Normal-Distribution Terminology Notation – Should ‘N’ in ‘Normal Distribution’ Be Capitalised in British English?

Question

This question is a bit left-field, but I figured that the community here probably has strong views on the subject!

I am writing up my PhD thesis. Consistently, when talking about quantities which are formally related to a Gaussian distribution, I have capitalised the "N" in "Normal" to refer to them. For example, "[…Under such circumstances] the resulting distribution is not Normal, but rather described by […]".

My supervisor has read through the relevant chapter, and replaced every single one of these with a lower-case 'n'. I can't find any definitive literature on the subject — Springer apparently wanted names properly capitalised, and according to another random dude on the internet, capitalising distribution names is a Good Idea.

Lacking a definitive style guide for my thesis, I thought I'd turn to the community of experts — what is commonly done, and why?

Answer 1

For what it's worth, Wikipedia says this on the origin of the name:

Since its introduction, the normal distribution has been known by many different name... Gauss himself apparently coined the term with reference to the "normal equations" involved in its applications, with normal having its technical meaning of orthogonal rather than "usual". However, by the end of the 19th century some authors had started using the name normal distribution, where the word "normal" was used as an adjective...

https://en.wikipedia.org/wiki/Normal_distribution#Naming

It is also not capitalized in the Wikipedia article, nor have I seen it capitalized in general as an American English speaker. For all intents and purposes normal IS an adjective, though not one that's meant to imply all other distributions are 'abnormal'.