[office-formula] domain for x in HYPGEOMDIST(x;n;M;N)

[Regina Henschel <rb.henschel@t-online.de>]

Hello members,

in OpenFormula-v1.2-draft11.odt chapter 6.17.36 HYPERGEOMDIST you define 
the constraints for x, "x<=M, x<=n, n<=N, M<=N with x,n,M,N >=0."
And you define HYPGEOMDIST(x;n;M;N) itself as
binom(M x)*binom(N-M n-x)/binom(N n).

I'll describe an example to show the problems.
Example: You have got an urn with M=6 white marbles and 4 black marbles, 
which is N=10 marbles total. You draw marbles n=7 times without 
replacement. Define the random variable X as "number of white marbles in 
the draw". What is the domain of X?

I can imagine two answers.
(A) The way Excel and OpenOffice.org use it: Constrain x to those 
numbers, which can be calculated with the given formula, using binom(a 
b) in a way, that it requires a>=b>=0. Doing this, you get the domain
max(0;n-N+M)..M
(B) The way Gnumeric uses it: Use the domain 0..n. For x<n-N+M and for 
x>M the probability is 0. That is the same result as using a tree 
diagram. You have branches with probabilty 0, for example for x=7 
because the urn contains only 6 white marbles or for x=1 because you 
will get at least 3 white marbles.

But in the spec those alternatives are mixed. For example the call 
HYPERGEODIST(1;7;6;10) is valid in respect to the constraints, but will 
cause an error in the factor binom(4 6) in the formula binom(6 
1)*binom(4 6)/binom(10 7).

Because the method(B) eases the use of the function HYPGEOMDIST and fits 
to the widespread explanation via tree diagram, constraints and formula 
should be changed to method(B). You need constraints
"x<=n, n<=N, M<=N with x,n,M,N >=0" and a case distinction in the formula
"For case max(0;n-N+M)<=x<=M result is binom(M x)*binom(N-M n-x)/binom(N 
n), for all other cases result is 0."

kind regards
Regina Henschel