Boost C++ Libraries: Ticket #12407: typos/bugs in arcsine CDF and support?

owner, component changed

Michel Morin — Fri, 26 Aug 2016 13:36:54 GMT

owner changed from Matias Capeletto to John Maddock
component Documentation → math

cc, status changed; resolution set

John Maddock — Sat, 27 Aug 2016 18:06:51 GMT

cc pbristow@… added
status new → closed
resolution → fixed

Thanks I've fixed the typo in Git.

WRT to the second question, Wikipedia has support over [0,1], and indeed PDF and CDF are perfectly calculable there, albeit the PDF is infinite at the limits. So I guess this comes down to taste?

Paul A. Bristow — Mon, 29 Aug 2016 09:03:29 GMT

Sorry to come late to this (been away). I think we can probably provide support for [0,1]. I'll check this out and say when I've done that (or decided why not). Won't be in the upcoming release, but will be committed to develop as soon as the release is out in case you wanted to pick up earlier.

anonymous — Mon, 29 Aug 2016 11:38:17 GMT

Paul, I think you have this the wrong way around: we *do* support the end points of the range already, the argument was that these should actually be undefined... but different sources seem to have different views on that.

John.

Paul A. Bristow — Tue, 30 Aug 2016 10:49:02 GMT

OK - I said I'd do some homework, and I have, starting with reading the original post and grabbing hold of the right end of the stick ;-)

https://reference.wolfram.com/language/ref/ArcSinDistribution.html warns of "PDF ... potential singularities (where it asymptotically approaches infinity) at points near both xmin and xmax" but is quiet about what happens at the max and min.

So I agree with John on this issue, and supporting [0, 1] is consistent with other Boost math implementations.

I think it provides the most convenient match of the infinite precision math to the digital floating-point implementation. We signal the singularity by returning infinity rather than throwing an exception (or whatever) to the input. We think this is commonly convenient for users.

Users can very easily intercept values that are at the min or max before the PDF or CDF call if they wish to catch and handle this in some different way.