Talk:Probability-generating function

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Mathematics B‑class Mid‑priority

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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).

What on earth does the notation G(1-) mean? It's used all over this article, and I've never seen it anywhere before. Is it supposed to be G(-1)? Or G(1)? Or is it just a typo? Could someone clarify/correct it please.

I hadn't seen it before but it is defined in the article. It is the limit as z->1 of G(z). Since this is used so much it is useful to have a shorthand though I have not seen this one before. --Richard Clegg 18:15, 4 June 2006 (UTC)[reply]

I'm not sure, but doesn't it mean the limit of G(x) as x approaches 1 from below? PAR 18:25, 4 June 2006 (UTC)[reply]

I think it is just a "typo". BM

The relation to "moment generating function"

Some Wikipedia articles about discrete random variables such as "Geometric distribution" use the term "moment generating function" instead of "probability generating function". So it would be useful to state that these are equivalent ideas in such cases.

edit; I don't mean "equivalent ideas". I should say "related ideas". My thought is that it would be useful to tell a reader if he can get the formula for the probability generating function by looking at the formula for the moment generating function since the articles favor giving the moment generating function.