[R] Possible problem with pbirthday

[A.G. Lynch]

Dear all

I have come across the following problem with pbirthday:
(I have observed this in R 1.9.1 and R 2.0.1 on the Windows OS)

As I understand it, pbirthday(n,c,k) gives the approximate probability 
that we see a class with k coicident people in it when n people are sorted into 
c classes.

so the command

> pbirthday(4,classes=3,coincident=4)

should give the approximate probability that when four people fall into 
three classes, all four end up in the same class. A probability 
that is clearly lower than the presently returned value of 1.


It seems to me that the line in the function

if (n > classes) return(1)

is only relevant to the default case of coincident = 2. (Naturally, if 
there are more people than classes, then at least one class must contain 
2 people).


Since the pbirthday function has been generalized to accept 
other values for coincidence

if (n > (classes * (coincident-1))) return(1)

would seem to me to be (one version of) the necessary line.


Alternatively I could be getting entirely the wrong end of the stick.

If you could either confirm or disabuse then I would be grateful

Yours

Andy Lynch

Centre for Applied Medical Statistics
Department of Public Health and Primary Care
University of Cambridge
Institute of Public Health