R devel - Feb 2008 - choose incorrect for fractional and some negative integer values (PR#10766)

Full_Name: Jerry W. Lewis
Version: 2.6.2
OS: Windows XP Professional
Submission from: (NULL) (198.180.131.16)


choose() returns incorrect values for all fractional arguments, regardless of
sign.  It returns 0 when both arguments are negative integers, which is not
always correct (as in some formulations of the negative hypergeometric).

Examples (correct answers from Maple's binomial function):

choose( 4.75,2.75)  # should be 8.90625
choose(-0.75,-0.5)  # should be 1.6692536833481464
choose(-1.75,-0.5)  # should be 0.55641789444938212
choose(-2.75,-1.5)  # should be 0.15897654127125204
choose(-5,   -7)    # should be 15

The correct answers for first two can be verified easily since choose(n,k)
should equal
  1/beta(n-k+1,k+1)/(n+1)
but does not for fractional arguments.  The latter three are instances where
beta incorrectly returns NaN, as noted in PR#10763

<Jerry.Lewis <at> biogenidec.com> writes:
> 
> Full_Name: Jerry W. Lewis
> Version: 2.6.2
> OS: Windows XP Professional
> Submission from: (NULL) (198.180.131.16)
> 
> choose() returns incorrect values for all fractional arguments, regardless
of
> sign.  It returns 0 when both arguments are negative integers, which is not
> always correct (as in some formulations of the negative hypergeometric).
> 
> Examples (correct answers from Maple's binomial function):
> 
> choose( 4.75,2.75)  # should be 8.90625
  [snip]

  The help page does say that k is supposed to be an integer -- so
I don't think this is a bug.
  Should the function either (a) test for k == (or close to ==) an integer
or (b) be rewritten to work more generally?

  Ben