Talk:Probability-generating function

The listed p.g.f for negative binomial is wrong. There should be no $z$ on the numerator, i.e.

$\left({\frac {p}{1-qz}}\right)^{r}$

It all depends on whether you are after the number of trials required to achieve n successes (which is at least n) or the number of failures before the nth success (which may be 0). From a quick check of the article geometric distribution, what you suggest above is correct for the latter definition, while the formula in the article is consistent with the text, which refers to the former. Ben Cairns 03:11, 2 Mar 2005 (UTC).