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Although similar questions have been already posed and answered here, I still have this doubt: in the case of initialisms written in lowercase (and possibly having full stops after each letter), how should we write their plurals? Should we be using an apostrophe before the 's'; no apostrophe; no 's' at all...?


EXAMPLE 1: The term random variable is usually abbreviated as r.v. So, several random variables could be referred to as r.v.'s?? If not, how?

EXAMPLE 2: Cumulative distribution function is usually abbreviated as c.d.f.; or even cdf, very often.

EXAMPLE 3: Very famous in Maths: greatest common divisor is usually abbreviated as gcd.


This question differs from previous ones in that I am interested in the plural of initialisms / acronyms written in lowercase.

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    Apostrophe means only two things. 1) omitted letters 2) posessive. Does this satisfy either of those? Commented Oct 25, 2019 at 18:05
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    @DJClayworth, depends on your style guide. The New York Times style guide says, "Use apostrophes for plurals of abbreviations that have capital letters and periods: M.D.’s, C.P.A.’s." afterdeadline.blogs.nytimes.com/2010/04/13/faqs-on-style
    – Juhasz
    Commented Oct 25, 2019 at 18:37
  • @Juhasz It certainly does. Some 'authorities' even allow an apostrophe in the pure plurals of [a very few odd] words (ex's; do's). Commented Oct 25, 2019 at 18:39
  • I can't find lowercased rv for random variable, but even the US-based dictionaries seem to be dropping the periods from the initialism RV (recreational vehicle). The plural is given as RVs (Collins); RVs or RV's (Wiktionary). Commented Oct 25, 2019 at 18:46
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    This is about style, not about grammar. In any particular case a style guide might be prescribed and that will tell you what to do (however daft its precepts might be). FWIW all those periods and apostrophes look clunky to some modern readers who do not see what is wrong with RVs, CDFs and so forth. Unless some style guide rules you, you do not have to choose lower case for the abbreviation of the singular: stick to upper case and add a lower case 's' for the plural.
    – JeremyC
    Commented Oct 25, 2019 at 21:54

1 Answer 1

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One approach, from what seems an immaculate publication from San Jose State University › faculty › gerstman {B. Burt Gerstman, D.V.M., M.P.H., Ph.D. Professor Emeritus}:

4: Probability ...

...

  • pdf: probability density function

  • pmf: probability mass function

  • RV: random variable

...

[p 2] Binomial random variables are discrete RVs of “counts” that describe the number of “successes”

...

[p 4] Probability mass functions (pmfs) can be drawn as pmf histograms.

...

[p 5, bottom] For additional instruction on pdfs see §5.4 in Basic Biostatistics for Public Health Practice (Gerstman 2015, Jones & Bartlett, Burlington, MA).

(1) This is one suggestion; you can probably find others. From the next nearest educational establishment, perhaps, with equally immaculate publications. There are usually in-house specifications (which are not universally binding ... merely university-binding).

(2) Note that periods are not used here in initialisms (these are not acronyms in the most usually accepted default sense of the word, as individual letters are read out; contrast NATO); this is standard practice in the UK for all abbreviations where there are not compelling reasons to add a full stop, and is catching on quite rapidly in the States. Stan Carey at WordPress offers advice on cases where periods are opted for.

(3) Note that capitalisation seems to follow arbitrary tradition rather than strict logic.

(4) The 'rule' used here is 'simply add a lower-case s to pluralise any initialism/acronym, no matter what the case is.' I'd go with this myself, but would reserve the right to insert an apostrophe where I felt it would aid clarity.

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  • As a nonnative speaker, I feel more comfortable with rv's pmf's than rvs and pmfs.
    – Vicent
    Commented Oct 27, 2019 at 23:07
  • I believe that the apostrophes in abbreviations like rv's, pdf's are becoming increasingly old-fashioned looking. Certainly CD's, RV's look very dated. But surely anyone writing RVs (= random variables) or pdfs has an in-house style guide or a tutor that will give the recommended style choice? They mustn't demand that others should not choose a different available style, of course. On ELU, it should be pointed out when different practices / understandings are also available, though ones considered better can of course be pointed out as such. I've said what I consider better. (Native speaker.) Commented Oct 28, 2019 at 16:06

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