@Silverfish: In "t distribution", or "Weibull distribution", "t" & "Weibull" are nouns being used attributively as adjectives. Fair enough, but give some people an inch & they'll take a mile, so we see "t distributed" & "Weibull distributed" - with "t" & "Weibull" as adverbs - now & again. Nevertheless the possessive modifier "Student's" is a strong enough reminder of "t"s true role that to write "Student's t distributed" really needs a brass neck or a tin ear. What about "t-ishly distributed"?
@scortchi Yes, that is how I would parse it as well. And it's funny how the "'s" disappeared. I imagine "Student-t distributed" is non-standard but I've certainly seen it. In contrast I can't recall seeing (and google doesn't pick up any substantial numbers of) "Snedecor's F distributed" or "Snedecor-F distributed" or similar (though admittedly even "Snedecor's F distribution" is fairly rare).