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min/max or infimum/supremum #150
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My preference is to use |
I agree with @johnmyleswhite. Using |
I'm cool with that too, despite the mathematical incorrectness. |
ok, I wouldn't care for correctness if it wasn't screwing up semantics too much. As mentioned in #126, I think it would be elegant to be able to implement |
I'm curious as to the rationale for needing to distinguish between an open interval and its closure: mathematically, the uniform distribution on [0,1] and the uniform distribution on (0,1) are identical. In what case would the need for this distinction arise? The whole concept of support isn't really a natural fit for probability anyway, it's really an analysis/topological concept in terms of functions, and trying to define it in terms of probability/measures is rather convoluted (interestingly, that article defines it as a closure anyway, which would make this whole minimum vs infimum argument redundant). |
Bah, [the linked Wikipedia article](https://en.wikipedia.org/wiki/Support_(measure_theory%29) says @simonbyrne is right. So actually the code in beta.jl |
@ingmarschuster mentioned in #126 that
min(d)
andmax(d)
is not appropriate for distributions whose support is an open interval.This is true in theory.
Here, we have to make a decision, between the following options:
min
andmax
, and documents that these functions return infimum and supremum when the domain is open.infi
andsupr
(orinfimum
andsupremum
). When the domain is closed, this still makes sense (in such cases, infimum equals the minimum and supremum equals maximum).cc @johnmyleswhite @dmbates
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