[R] Curious Behavior with Curve() and dnorm()

[Prof Brian Ripley]

For which x do you think sd(x) is evaluated?

Hint: the help page shows

     expr: an expression written as a function of 'x', or alternatively
           the name of a function which will be plotted.

and you have written dnorm(x, mean=mean(x), sd=sd(x)) as function of x.


On Thu, 10 Feb 2005, Thomas Hopper wrote:

> I am attempting to wrap the histogram function in my own custom function, so 
> that I can quickly generate some standard plots.
>
> A part of what I want to do is to draw a normal curve over the histogram:
>
>> x <- rnorm(1000)
>> hist(x, freq=F)
>> curve(dnorm(x), lty=3, add=T)
>
> (for normal use, x would be a vector of empirical values, but the rnorm() 
> function works for testing)
>
> That works just as you'd expect, but I've found something a bit strange.
>
> If I try the following:
>
>> curve(dnorm(x, mean=mean(x), sd=sd(x)), lty=3, add=T)
>
> I get a much flatter and broader curve (which looks like it probably has the 
> same area as the first curve, though I haven't tested).
>
> However, if I do
>
>> z <- sd(x)
>> curve(dnorm(x, mean=mean(x), sd=z), lty=1, add=T)
>
> I get the curve you'd expect; it draws right over the first curve 
> (curve(dnorm(x),...), above).
>
> I haven't touched x between the call to curve() containing 
> dnorm(...,sd=sd(x)) and the call to curve() containing dnorm(...,sd=z), and 
> tests show that z == sd(x).
>
> I get similar results if I manually type in the standard deviation of x--the 
> expected curve is drawn--so the broader and flatter curve is only drawn when 
> I call dnorm with sd=sd(x).
>
> Is there a reason for this, or is there something odd going on with the call 
> to curve()?

It's working as documented.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595