[R] rootogram for normal distributions

[Achim Zeileis]

On Sun, 16 Jan 2011, Hugo Mildenberger wrote:

> Using R-2.12.1 and latticeExtra-0.6-14, I would like to understand
> why a rootogram displaying samples from the Poisson distribution looks like I
> expected it, whereas a rootogram using the normal distribution does not:
>
> library(latticeExtra)
> rootogram(~rpois(1000, lambda = 50), dfun = function(x) dpois(x, lambda = 50))
>
> rootogram(~rnorm(1000), dfun = function(x) dnorm(x,mean(x),sd(x)))
>
> I probably can't attach figures here. Thus a textual description of what 
> I get may suffice: With increasing sample size, the rootogram using 
> random samples from the Poisson distribution shows decreasing 
> differences (bars are quickly approaching the zero line), whereas the 
> displayed differences for random samples of the normal distribution are 
> always large. The differences even increase with sample size, i.e, the 
> hanging bars tend to vanish for very large samples.

The normal distribution is a continuous distribution, i.e., the frequency 
for each observed value will essentially be 1/n and not converge to the 
density function. Hence, you would need to look at histogram or smoothed 
densities. Rootograms, on the other hand, are intended for discrete 
distributions.
Z

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