[R] Why does qt() return Inf with certain negative ncp values?

[Martin Maechler]

>>>>>     on Mon, 13 Jun 2022 19:28:43 -0700 writes:

    > Well, this will likely require close numerical analysis of
    > the algorithm used for the calculation, which I can't help
    > with, but I do note for the first case (I didn't bother
    > checking the second) it may be useful to note that besides
    > returning Inf, I also got with -7 as ncp:

    > "There were 50 or more warnings" all of which were: "In
    > qt(1 - 1 * (10^(-11)), 35, -7) : full precision may not
    > have been achieved in 'pnt{final}' "

    > I got this warning for all the other values of ncp also.

    > So it looks like: Congratulations, you seem to have
    > defeated the algorithm.

    > Bert Gunter

Thank you, Bert, for the extra information and Stephen  for
reporting.

[@Stephen:  no reason to use sapply(); qt() etc are all vectorized!]

Part of this is "known in principle" 
as the help page mentions in several places that the non-central t
algorithm for pt() has deficiencies and
that in the non-central case, qt() is defined by  inversion,
i.e., a (primitive !) version of uniroot(), using pt(*, ncp=.) :


> Note :
>      The code for non-zero ‘ncp’ is principally intended to be used for
>      moderate values of ‘ncp’: it will not be highly accurate,
>      especially in the tails, for large values.

and indeed, you use values very much "in the tails".
and that *does* give a warning, as Bert mentioned.
[ You really should heed such warnings.
  {{careless people using  suppressWarnings() all the time is
    really very irresponsible programming/scientific practice!
  }}]
    
>>>>>     on Mon, 13 Jun 2022 19:28:43 -0700 writes:

    > Well, this will likely require close numerical analysis of
    > the algorithm used for the calculation, which I can't help
    > with, but I do note for the first case (I didn't bother
    > checking the second) it may be useful to note that besides
    > returning Inf, I also got with -7 as ncp:

    > "There were 50 or more warnings" all of which were: "In
    > qt(1 - 1 * (10^(-11)), 35, -7) : full precision may not
    > have been achieved in 'pnt{final}' "

    > I got this warning for all the other values of ncp also.

    > So it looks like: Congratulations, you seem to have
    > defeated the algorithm.

    > Bert Gunter

Thank you, Bert, for the extra information and Stephen  for
reporting.

[@Stephen:  no reason to use sapply(); qt() etc are all vectorized!]

Part of this is "known in principle" 
as the help page mentions in several places that the non-central t
algorithm for pt() has deficiencies and
that in the non-central case, qt() is defined by  inversion,
i.e., a (primitive !) version of uniroot(), using pt(*, ncp=.) :

    Note :
         The code for non-zero ‘ncp’ is principally intended to be used for
         moderate values of ‘ncp’: it will not be highly accurate,
         especially in the tails, for large values.

and indeed, you use values very much "in the tails".
and the use *does* give warning, as Bert mentioned.
You really should heed such warnings.
{{careless people using  suppressWarnings() all the time is
  really very irresponsible programming/scientific practice!   }}
    
There's much more to be said here, but as I see  Stephen has in
the mean time diverted the topic to the  R-devel mailing list --
quite appropriately -- 
  --> https://stat.ethz.ch/pipermail/r-devel/2022-June/081785.html

I will answer there.

Best,
Martin

--
Martin Maechler
ETH Zurich  and  R Core team