<p><strong>For the record:</strong> our tag description for <a href="https://stats.stackexchange.com/questions/tagged/pdf" class="post-tag" title="show questions tagged &#39;pdf&#39;" rel="tag">pdf</a> has always said that one should use it for PMFs too. When you created <a href="https://stats.stackexchange.com/questions/tagged/pmf" class="post-tag" title="show questions tagged &#39;pmf&#39;" rel="tag">pmf</a> tag yesterday to replace <code>[pdf]</code> <a href="https://stats.stackexchange.com/questions/240720">on one of the questions</a>, I rolled your edit back because I thought you are clearly going against our established usage. When you immediately replaced it <em>back</em>, I got a bit annoyed and flagged the post for mod attention suggesting to make <code>pmf</code> the synonym of <code>pdf</code>. @Gung must have seen my flag and decided to act on it.</p>

<p>Now, I agree with Tim that</p>

<blockquote>
  <p>I can't see any problem with making [pdf] and [pmf] synonyms. The idea of synonyms is not only about exact synonyms, but about groupping related concepts for easier searching.</p>
</blockquote>

<p>That said, I think we <em>could</em> keep them separate if we wanted. For this we would need (1) to remove the synonym mapping, and (2) to retag all Qs about PMFs that are tagged [pdf]. It turns out it's not so many: I get only 24 Qs with these two searches: <a href="https://stats.stackexchange.com/search?q=%5Bpdf%5D+is%3Aquestion+%22pmf%22">one</a> and <a href="https://stats.stackexchange.com/search?q=%5Bpdf%5D+is%3Aquestion+-%22pmf%22+%22probability+mass%22">two</a>. I expected to find many more, but 24 are easily doable in a couple of days. </p>

<p>I don't have a strong opinion and am fine with it either way.</p>

<p>Personally, I don't see the difference between PDF and PMF particularly important because if one allows delta functions then these two concepts can be combined together. See <a href="https://en.wikipedia.org/wiki/Probability_density_function#Link_between_discrete_and_continuous_distributions" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Probability_density_function#Link_between_discrete_and_continuous_distributions</a>. As always with delta functions, a little extra care is needed to do it in a mathematically rigorous way (see <a href="https://math.stackexchange.com/a/54249">https://math.stackexchange.com/a/54249</a>), but in practice one does not need to bother because it behaves in an intuitively clear way.</p>
