[R] Off topic --- underdispersed (pseudo) binomial data.

Abby Spurdle @purd|e@@ @end|ng |rom gm@||@com
Fri Mar 26 01:41:00 CET 2021

I haven't checked this, but I guess that the number of students that
*pass* a particular exam/subject, per semester would be like that.

Let's say you have a course in maximum likelihood, that's taught once
per year to 3rd year students, and a few postgrads.
You could count the number of passes, each year.

If you assume a near-constant probability of passing in each exam/semester:
Then I would assume it would follow the distribution that you're requesting.

If there is a significant change in the number of students:
Lets say, that less and less students study maximum likelihood because
they would rather study "advanced" R programming for "data science"
with "large data", then you might be able to apply some sort of
discrete-scaling transformation to the number of passes each semester.
This would allow you to pretend that the number of people studying
maximum likelihood is the same, and no one is studying other
apparently more important subjects.

On Thu, Mar 25, 2021 at 2:33 PM Rolf Turner <r.turner using auckland.ac.nz> wrote:
> I would like a real-life example of a data set which one might think to
> model by a binomial distribution, but which is substantially
> underdispersed. I.e. a sample X = {X_1, X_2, ..., X_N} where each X_i
> is an integer between 0 and n (n known a priori) such that var(X) <<
> mean(X)*(1 - mean(X)/n).
> Does anyone know of any such examples?  Do any exist?  I've done
> a perfunctory web search, and had a look at "A Handbook of Small
> Data Sets" by Hand, Daly, Lunn, et al., and drawn a blank.
> I've seen on the web some references to underdispersed "pseudo-Poisson"
> data, but not to underdispersed "pseudo-binomial" data.  And of course
> there's lots of *over* dispersed stuff.  But that's not what I want.
> I can *simulate* data sets of the sor that I am looking for (so far the
> only ideas I've had for doing this are pretty simplistic and
> artificial) but I'd like to get my hands on a *real* example, if
> possible.
> Grateful for any pointers/suggestions.
> cheers,
> Rolf Turner
> --
> Honorary Research Fellow
> Department of Statistics
> University of Auckland
> Phone: +64-9-373-7599 ext. 88276
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