Re: [SPSSX-L] Negative Binomial – SPSS Bug (?)

Posted by SD on Sep 27, 2012; 11:04am
URL: http://spssx-discussion.165.s1.nabble.com/Negative-Binomial-SPSS-Bug-tp5715014p5715310.html

Hello,

I have the same problem like Frank and I don't manage to solve it.

Regarding to http://pic.dhe.ibm.com/infocenter/spssstat/v21r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.help%2Fsyn_transformation_expressions_random_variable_distribution_functions.htm , http://pic.dhe.ibm.com/infocenter there is used a density formula, which uses an other definition of the negative Binomial distribution than the one from the source from Frank [1].

Since I have the expected value E and the Variance V, I want to compute the two parameters probability p and the threshold r.

For the in SPSS used definition, I found
E=r/p
V=r*(1-p)/p²
(found at http://de.wikipedia.org/wiki/Negative_Binomialverteilung#Erwartungswert, sorry for the german link, I just didn't found this in english.)

Derived from this I get
p=1/(V/E +1)
r=E*p

But this results in two problems:
One is, that there are different results than with the variant from Franks source.

The other is that like this, p is always <1/2 (since V/E>1, over dispersion) and resulting from this, if E<=2, then r<1, then SPSS Error.

Thank you in advance,
Silvio.

Literature:
[1] Schlittgen, R.: Einführung in die Statistik. 5. Auflg.  Oldenbourg 1995,
S.203 ff