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I confess that I made a new tag: identity. A search of 'identity' on the main site yielded 1110 questions, and being able to label something as an identity and search for it is a good thing. Identities are extremely important when writing new statistical density functions, and can disguise two expressions that are equal, but not recognizably so. When I develop new pdf's, CDF's, expected values, and the like, I keep a separate list of useful identities that makes it possible for me to work through those statistical formulas.

Identities are important to note explicitly because if you do not know them by heart, or at least recognize that they might exist for a function, you will be stuck completely doing integration (e.g., CDF finding), simplification, expectation, proofs, and other mathematical steps. Almost any class of functions has numerous identities the existence of which should be known to do novel statistical development work. For example, hyperbolic functions have numerous identities.

So, question is, what do you think about identity as a new tag? See Understanding an Estimator Identity as an example.

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    $\begingroup$ Personally, I do not see how this tag should be useful or helpful. Do you intend to create [equality], [inequality], [formula], [expression] as well? $\endgroup$ – amoeba Nov 8 '16 at 8:46
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    $\begingroup$ @amoeba Summarizing, you do not find identity to be an unusually important concept, nor do you differentiate identity from the other search terms you mockingly put forward. I do not intend to create equality, inequality, formula, or expression. The importance of identities has become more apparent to me the more I have explored hitherto uncharacterized distributions and physically relevant novel statistical physics. I would suggest that if you were to do likewise, you would understand better why I hold identities in high esteem. $\endgroup$ – Carl Nov 8 '16 at 16:31
  • $\begingroup$ Well, I'd say let's wait and see if people are going to support your new tag. Until then I'd suggest you do not do much re-tagging. $\endgroup$ – amoeba Nov 8 '16 at 16:37
  • $\begingroup$ @amoeba Not at all. My thought was "Wow, how many important identities there are in statistics, for example for expected value; we should have a tag for that; it would be very useful." I am not trying to convince you. Each to his own. $\endgroup$ – Carl Nov 8 '16 at 16:46
  • $\begingroup$ @amoeba Sorry, I put the tag on the main site. My creating it on the Meta site was carelessness on my part. $\endgroup$ – Carl Nov 8 '16 at 16:48
  • $\begingroup$ @amoeba I took identity off the Meta site $\endgroup$ – Carl Nov 8 '16 at 16:50
  • $\begingroup$ @amoeba Why do you not answer that you do not like the tag, so I can vote it down? $\endgroup$ – Carl Nov 8 '16 at 19:37
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    $\begingroup$ Like @amoeba, I don't see any value in having an [identity] tag. One thing that might help is if you made a tag excerpt for it. It isn't remotely clear to me what the tag is supposed to be for, or how to decide if it picks out anything of value about a question. Is the idea that it should be on any thread that includes an equals sign? $\endgroup$ – gung Nov 8 '16 at 21:18
  • $\begingroup$ @gung Hardly. I gave an example in the question. I find it astounding that I am getting so little support on this. This tag already exists on the math.stackexchange.com/questions/tagged/…, was used 5 times this month on that site and also has no description on that site. Why? It is obvious to a student mathematician (the math.stackexchange.com site is not mathoverflow.net; the professional site) what it is and why it is so important. I can make a tag description here, only if our site expresses a student's level appreciation of the identity. $\endgroup$ – Carl Nov 9 '16 at 20:37
  • $\begingroup$ @gung I put in more information about identities in my question. Seriously, if all one does with statistics is learn what others have done, then 90% of the fun goes la-la. The real fun is making up completely new stuff, and for that you need identities. $\endgroup$ – Carl Nov 9 '16 at 21:17
  • $\begingroup$ Re Math.SE: the [identity] tag there was used 5 times ever; it seems it's a stray tag that was only created this month, perhaps accidentally. It lacks a tag description not because its meaning is obvious for users of that site but because it's a tag that nobody cares about (and nobody cared to create until this month). $\endgroup$ – amoeba Nov 9 '16 at 21:34
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    $\begingroup$ As a general rule, every tag should have an excerpt, no matter how obvious it seems to you. If you create a tag, you should add an excerpt. Consider that novice users will possibly end up adding [identity] on questions like 'how to add an ID variable to my panel data since it's in long format', or some such. $\endgroup$ – gung Nov 9 '16 at 22:05
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    $\begingroup$ The excerpt is helpful, so I'll remove my downvote. $\endgroup$ – gung Nov 10 '16 at 14:04
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    $\begingroup$ "An identity is a generally non-intuitive equivalence between two mathematical expressions." This excerpt definitely helps a lot. $\endgroup$ – stats0007 Nov 16 '16 at 18:50
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    $\begingroup$ But I am still not 100% convinced...I somehow agree with @amoeba, that the concrete, complete scope of this tag would seem unclear to me. $\endgroup$ – stats0007 Nov 16 '16 at 18:53
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There are multiple good reasons mentioned in the comments, but let me add my five cents, especially as you pinged me on my own question

So, we promote the identity function for convolution to tag status, but not the identity meta.stats.stackexchange.com/questions/4440/…. So, we name individual leaves, and ignore their tree. What, I muse, would we do with a whole forest? LOL.

I guess that you mention the reason why your proposal was downvoted. Such tag would be too broad to be helpful. Using your own example, [forest] tag is not helpful if you are looking precisely for [blueberries], or [mushrooms], and if you are looking for mushrooms in the forest, then since they are a subset of items in the forest, it is enough to search for them directly. I guess that if you are looking for information involving identity, then you are not interested in going through all the possible identities in probability theory, but an identity that is connected to some specific problem of your interest.

Moreover if we had [identity] tag, then maybe we also should create other tags as: [equality], [ineqality], [integral], [axiom] etc. What if you asked a question that involved using some axioms, identities, inequalities and calculating integrals? Would using all those tags be really needed in here? How would you decide which of those tags are more important then others?

You could check also Tag-candidates for removal thread or go through other discussions about tags to see why we deleted or considered deleting other tags. In general, too specific, or too broad tags are often considered not very useful.

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  • $\begingroup$ What I was getting at is the identity function of an algebra. Most people have not studied abstract algebra so would not know that the basis of any algebra is the identity function, and thus how that function is fundamental to any other manipulation made within that algebraic construct. That our readers are unimpressed with how pivotal the identity concept is, is underwhelming. $\endgroup$ – Carl Aug 8 '17 at 0:29

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