Here is an email sent by one of my students a few days ago:
Do you know how to integrate a function with an “if”?
For instance:
>X=rnorm(100)
>Femp=function(x){
+ return(sum(X<x))
+}
>integrate(Femp,0,1)$valuedoes not work.
My reply was that the fundamental reason it does not work is that integrate (or curve for instance) computes the function in several points of a grid by calling the function on a vector x and the comparison X<x does not make sense when both X and x are vectors. If one rewrites the code as
[sourcecode language=”r” gutter=”false”]
X=rnorm(100)
Femp=function(x){
return((apply(as.matrix(outer(X,x,"-")<0),2,sum))}
[/sourcecode]
the function can be integrated
[sourcecode language=”r” gutter=”false”]
> integrate(Femp,-2,2)
1.877735 with absolute error < 5.6e-05
[/sourcecode]
However, this kind of syntactic gymnastic can be avoided by a simple call to Vectorize.
[sourcecode language=”r” gutter=”false”]
X=rnorm(100)
Femp=function(x){
return(sum(X<x))}
> integrate(Vectorize(Femp),-2,2)
1.877735 with absolute error < 5.6e-05
[/sourcecode]
