Talk:Conway–Maxwell–Poisson distribution

Can someone explicate recisive formula for the moments? In particular the case r = 0 looks confusing as to what it meansd and how it is meant to be used. Perhaps it would help to define the moments as a function of the parameters and then give an explicit expression in terms of this function. Melcombe (talk) 08:51, 18 September 2008 (UTC)

Eponyms??
This article says:
 * Typically, the negative binomial distribution is used to model data with over-dispersion, however the Conway–Maxwell–Poisson (CMP) distribution provides an improved, yet relatively unknown, alternative.
 * Typically, the negative binomial distribution is used to model data with over-dispersion, however the Conway–Maxwell–Poisson (CMP) distribution provides an improved, yet relatively unknown, alternative.

You see the conspicuous omission: obviously it should say:
 * Typically, the negative binomial distribution is used to model data with over-dispersion, however the Conway–Maxwell–Poisson (CMP) distribution, named after ?????? Conway, ?????? Maxwell, and ?????? Poisson, provides an improved, yet relatively unknown, alternative.
 * Typically, the negative binomial distribution is used to model data with over-dispersion, however the Conway–Maxwell–Poisson (CMP) distribution, named after ?????? Conway, ?????? Maxwell, and ?????? Poisson, provides an improved, yet relatively unknown, alternative.

It's obvious which "Poisson" is involved, and an obvious guess for the second eponym is James Clerk Maxwell, but which Conway is involved is less clear. Can someone fill in the blanks in the article? Michael Hardy (talk) 03:38, 20 October 2009 (UTC)


 * The Distribution is named after Richard W. Conway and William L. Maxwell, who wrote the book "Theory of Scheduling" (ISBN 0-486-42817-6) --217.91.126.201 (talk) 00:38, 23 December 2009 (UTC)

Cumulative distribution
Is there a notation error regarding the generalized hypergeometric function in the numerator as below?
 * $$ _1F_{\nu-1}(n+2,\ldots,n+2;\lambda) $$

Should the presence of the “index-prefix” 1 suppose arguments in F before the first “;” ?

Such as
 * $$\,{}_1F_q(a_1;b_1,\ldots,b_q;z) $$

What should $$a_1$$ be? — Preceding unsigned comment added by Scharleb (talk • contribs) 16:08, 23 December 2020 (UTC)

Over dispersion and under dispersion with respect to nu
I believe according to some external references that overdispersion is when nu<1 and overdispersion in the other case. Could this be confirmed and added, for example, in the first section. Thanks, — Preceding unsigned comment added by Scharleb (talk • contribs) 16:16, 23 December 2020 (UTC)