# Chi-square origin of the name

What are the origins of the names and letters in these distributions:

What is the origin of the name in chi-square distribution $$\chi_k^2$$?

And the origin of $$t$$ in student's $$t$$-test?

And naming $$Z$$ and $$\Phi$$ in normal distribution?

The other classes of distributions have more understandable names, but I have definitely forgotten some unnatural. You are welcome to suggest more weird names.

• What do you find "unnatural" or "weird" about these choices? Once upon a time--up until the Second World War, approximately--all people (in the West) with an advanced education had working knowledge of ancient Greek and Latin. Please note, too, that "$\Psi$" (capital Greek Psi) is rarely used in conjunction with the Normal distribution. Much commoner is "$\Phi$" (capital Phi--the Greek $F$). – whuber Nov 10 '18 at 16:37
• If your question is why Greek letters rather than, say, Hebrew or Cyrillic, part of the answer has been given by @whuber. The fact that studying Greek was quite common in universities means that the university printers had Greek letters to hand and were familiar with them. So it was easy for the authors and convenient for the printers to use Greek. – JeremyC Nov 10 '18 at 23:12
• As noted in the second-last paragraph here, Karl Pearson used $\chi^2$ to represent the term in the exponent of a multivariate normal density; its use for the chi-squared distribution and the chi-squared test follow from that. I don't know whether he got that use from someone else or invented that use himself (he certainly had a classical and a mathematical education so he could easily have done so), but it come into wide use because of him. He certainly uses it in 1900, though I expect it was being used before then. – Glen_b Nov 10 '18 at 23:22
• The t-test is called the t-test following notation used by Fisher in writing about it - Gosset (Student) wrote about it before Fisher but to my recollection didn't call it "t". Fisher showed that the t-statistic had a t-distribution; Gosset had good reasons to think it was the case (including using simulation of a sort) but didn't prove it. I think this is also discussed in an answer on site but I didn't turn it up yet. – Glen_b Nov 10 '18 at 23:27
• I'm not sure my references at that link relate to this (I do mention Fishers book there where I think he does cover it but that link isn't talking about that part). I think I gave a reference to Fisher (perhaps published in Metron, but perhaps that was one on the correlation coefficient instead) in a different answer that would apply though. I can't locate it now. But your link relates to correspondence around 1912 (I think) with Gosset which precedes anything I mention. – Glen_b Nov 11 '18 at 0:02