Random Count Generation with rnbinom

classic Classic list List threaded Threaded
2 messages Options
Reply | Threaded
Open this post in threaded view
|

Random Count Generation with rnbinom

Dario Strbenac-2
The documentation states :

An alternative parametrization (often used in ecology) is by the mean ‘mu’, and ‘size’, the dispersion parameter.

However, this fails :

> rnbinom(10, mu = 100, size = 0)
 [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
Warning message:
In rnbinom(10, mu = 100, size = 0) : NAs produced

For dispersion set to 0, it should work like drawing from a Poisson distribution.

It also produces incorrect draws for non-zero dispersions :

> rnbinom(10, mu = 100, size = 0.000001)
 [1] 0 0 0 0 0 0 0 0 0 0

It also fails for underdispersed count models :

> rnbinom(10, mu = 100, size = -0.1)
 [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
Warning message:
In rnbinom(10, mu = 100, size = -0.1) : NAs produced

> sessionInfo()
R version 3.0.2 (2013-09-25)
Platform: x86_64-pc-linux-gnu (64-bit)

locale:
 [1] LC_CTYPE=en_AU.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_AU.UTF-8        LC_COLLATE=en_AU.UTF-8    
 [5] LC_MONETARY=en_AU.UTF-8    LC_MESSAGES=en_AU.UTF-8  
 [7] LC_PAPER=en_AU.UTF-8       LC_NAME=C                
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_AU.UTF-8 LC_IDENTIFICATION=C      

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base    

loaded via a namespace (and not attached):
[1] tools_3.0.2

--------------------------------------
Dario Strbenac
PhD Student
University of Sydney
Camperdown NSW 2050
Australia
______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-devel
Reply | Threaded
Open this post in threaded view
|

Re: Random Count Generation with rnbinom

Achim Zeileis-4
On Sun, 23 Feb 2014, Dario Strbenac wrote:

> The documentation states :
>
> An alternative parametrization (often used in ecology) is by the mean ?mu?, and ?size?, the dispersion parameter.
>
> However, this fails :
>
>> rnbinom(10, mu = 100, size = 0)
> [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
> Warning message:
> In rnbinom(10, mu = 100, size = 0) : NAs produced
>
> For dispersion set to 0, it should work like drawing from a Poisson
> distribution.

No, Poisson is the case for size converging to Inf. Compare:

R> dnbinom(1:4, mu = 1, size = 1e9)
[1] 0.36787945 0.18393972 0.06131324 0.01532831
R> dpois(1:4, lambda = 1)
[1] 0.36787944 0.18393972 0.06131324 0.01532831

This is easy to see from the explanation in the manual page:

   The variance is 'mu + mu^2/size' in this parametrization.

So for size = Inf this yields mu, i.e., equidispersion. And for finite
positive size, there is always overdispersion.

> It also produces incorrect draws for non-zero dispersions :
>
>> rnbinom(10, mu = 100, size = 0.000001)
> [1] 0 0 0 0 0 0 0 0 0 0

This conforms with the documentation

   The case 'size == 0' is the distribution concentrated at zero.
   This is the limiting distribution for 'size' approaching zero,
   even if 'mu' rather than 'prob' is held constant. Notice though,
   that the mean of the limit distribution is 0, whatever the value
   of 'mu'.

> It also fails for underdispersed count models :
>
>> rnbinom(10, mu = 100, size = -0.1)
> [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
> Warning message:
> In rnbinom(10, mu = 100, size = -0.1) : NAs produced

And here the manual explains:

     size: target for number of successful trials, or dispersion
           parameter (the shape parameter of the gamma mixing
           distribution).  Must be strictly positive, need not be
           integer.


>> sessionInfo()
> R version 3.0.2 (2013-09-25)
> Platform: x86_64-pc-linux-gnu (64-bit)
>
> locale:
> [1] LC_CTYPE=en_AU.UTF-8       LC_NUMERIC=C
> [3] LC_TIME=en_AU.UTF-8        LC_COLLATE=en_AU.UTF-8
> [5] LC_MONETARY=en_AU.UTF-8    LC_MESSAGES=en_AU.UTF-8
> [7] LC_PAPER=en_AU.UTF-8       LC_NAME=C
> [9] LC_ADDRESS=C               LC_TELEPHONE=C
> [11] LC_MEASUREMENT=en_AU.UTF-8 LC_IDENTIFICATION=C
>
> attached base packages:
> [1] stats     graphics  grDevices utils     datasets  methods   base
>
> loaded via a namespace (and not attached):
> [1] tools_3.0.2
>
> --------------------------------------
> Dario Strbenac
> PhD Student
> University of Sydney
> Camperdown NSW 2050
> Australia
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-devel