# [R] Multivariate hypergeometric distribution version of phyper()

Karl Brand k.brand at erasmusmc.nl
Tue Mar 30 16:02:01 CEST 2010

```Dear R Users,

I employed the phyper() function to estimate the likelihood that the
number of genes overlapping between 2 different lists of genes is due to
chance. This appears to work appropriately.

Now i want to try this with 3 lists of genes which phyper() does not
appear to support.

Some googling suggests i can utilize the Multivariate hypergeometric
distribution to achieve this. eg.:

http://en.wikipedia.org/wiki/Hypergeometric_distribution

But when i try to do this manually using the choose() function (see
attempt below example with just two gene lists) i'm unable to perform
the calculations- the numbers hit infinity before getting an answer.

Searching cran archives for "Multivariate hypergeometric" show this term
in the vignettes of package's ‘combinat’ and ‘forward’. But i'm unable
to make sense of the these pachakege functions in the context of my
aforementioned apllication.

Can some one suggest a function, script or method to achieve my goal of
estimating the likelyhood of overlap between 3 lists of genes, ideally
using the multivariate hypergeometric, or anything else for that matter?

Karl

#example attempt with two gene lists m & n
N <- 45101 # total number balls in urn
m <- 720   # number of 'white' or 'special' balls in urn, aka 'success'
n <- 801   # number balls drawn or number of samples
k <- 40    # number of 'white' or 'special' balls DRAWN

a <- choose(m,k)
b <- choose((N-m),(n-k))
z <- choose(N,n)
print(prK)
[1] NaN

> a
[1] 7.985852e+65
> b
[1] Inf
> z
[1] Inf

--
Karl Brand
Department of Genetics
Erasmus MC
Dr Molewaterplein 50
3015 GE Rotterdam
T +31 (0)10 704 3457 | F +31 (0)10 704 4743 | M +31 (0)642 777 268

```