[Rd] Feature request: ..., binomial ... exact test efficiency improvements

[Kurt Hornik]

>>>>> Martin Maechler writes:

Hmm.  binom.test is documented to perform an "Exact Binomial Test" ...?

-k

>>>>> Chris Chang 
>>>>>     on Sat, 16 May 2026 14:24:19 -0700 writes:

> [............................]	  

>>> The one-sided binom.test() does not have this kind of
>>> performance problem, but the two-sided test (which can be
>>> written in a manner similar to qbinom(): instead of
>>> searching for minimal k satisfying pbinom(k, ...) >= p,
>>> search for the innermost opposite-tail k satisfying
>>> dbinom(k) <= dbinom(x)) does.
>>> 
>>> I can submit a patch with efficient two-sided binomial
>>> and Fisher's 2x2 exact test implementations if there is
>>> interest.
>>> 
>>> --Chris

> Dear Chris  (and other readers),

> Above, you also mention binom.test(),
> and indeed, when I choose numbers in the order of 1e8,
> I see binom.test() taking quite some time, e.g.,

>> system.time(btL <- binom.test(c(4e8, 1.01e8), p = 0.8, alternative = "two.sided"))
>    user  system elapsed 
>   8.306   0.837   9.159 

> and here, the time spent is really during p-value computation itself,
> everything else in binom.test() being very fast, AFAICS.

> Here it would be useful if you provide a patch to speed the
> p-value computation, still getting exact p-values, using
> pbinom() only instead of  dbinom(<large_support), ..).

> Traditionally, we as R core and any applied statistician would
> say that in such large N cases, simple normal approximations should be accurate enough,
> which it would be practically in any case, OTOH, it would still
> be nice to get the exact probabilities / confidence intervals,
> with a faster calulation.

> Eventually using a new argument  `exact = N < 1e6`  (for some N)
> and using a normal (or better!) asymptotic approximation for
> exact = FALSE  may make sense here as well...

> Thank you for raising the issue!

> With best regards,
> Martin

> --
> Martin Maechler
> ETH Zurich and  R Core team

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