[R] Simulation functions for underdispered Poisson and binomial distributions

[Charles C. Berry]

On Wed, 15 Jul 2009, Shinichi Nakagawa wrote:

> Dear R users
>
> I would like to simulate underdispersed Poisson and binomial distributions 
> somehow.
>
> I know you can do this for overdispersed counterparts - using rnbinom() for 
> Poisson and rbetabinom() for binomial.
>
> Could anyone share functions to do this? Or please share some tips for 
> modifying existing functions to achieve this.


Shinichi,

You really need a model for the underdispersion. Using that model, you 
would calculate the probabiltities fo the binomial or Poisson counts.

But you have to come up with something appropriate for your situation.

For example,

 	probs <- prop.table( dbinom( 0:10, 10, .5)^3 )

or

 	probs <- prop.table( dbinom( 0:10, 10, .5) +
 			ifelse( 0:10 == 5, 1, 0) )


will each produce probabilities for counts that are less dispersed than

 	probs <- dbinom( 0:10, 10, 0.5 )

but neither may suitably model the counts for the situation in which you 
are interested.

---

Once you have that model in hand

 	sample( 0:10, N, pr=probs, repl=TRUE )

will 'simulate' N such counts.

HTH,

Chuck


>
> Thank you very much for your help and time
>
> Shinichi
> ____________________
> Shinichi Nakagawa, PhD
> (Lecturer of Behavioural Ecology)
> Department of Zoology
> University of Otago
> 340 Great King Street
> P. O. Box 56
> Dunedin, New Zealand
> Tel:  +64-3-479-5046
> Fax: +64-3-479-7584
> http://www.otago.ac.nz/zoology/staff/academic/nakagawa.html
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901