Integration / Integral in R: Catch Search

Question

Well, so it confused me for more than 3 days and, without taking another step closer to the solution, I am going to try my luck here.

In the past, I wrote some code for one sorted dataset in a specific one, and it looks like this:

n <- length(data) maxobs <- max(data) minobs <- min(data) FG <- function(m=NULL, h = NULL){ n<- length(data) #Number of observations if (m<minobs){FG = 0} else { if (m >maxobs){FG = 1} else { FG = sum(pnorm((m - data)/h)-pnorm((minobs-data)/h))/sum(pnorm((maxobs - data)/h)-pnorm((minobs-data)/h)) }} return(FG) } f<- function(m,h){ f<- FG(m,h)^n return(f) } ##Integration max <- NULL delta<- function(h,max=maxobs){ delta <- integrate(Vectorize(f), minobs, max, h)$value return (delta) } 

which works PERFECTLY. For example, if you select the data: = c (1,2,3,4,5), you get the correct result for

 > delta(0.1, maxobs) [1] 0.6300001 

However, now I am trying to generalize it for each sorted data set, so what I did (it was clear: the data set x is sorted before all these functions are executed)

 FG <- function(x, m=NULL, h = NULL){ n<- length(x) #Number of observations maxobs <- max(x) minobs <- min(x) if (m<minobs){FG = 0} else { if (m >maxobs){FG = 1} else { FG = sum(pnorm((m - x)/h)-pnorm((minobs-x)/h))/sum(pnorm((maxobs - x)/h)-pnorm((minobs-x)/h)) }} return(FG) } f<- function(x,m,h){ n <- length(x) f<- FG(x,m,h)^n return(f) } ##Integration delta<- function(x,h,maxu= max(x)){ minobs <- min(x) delta <- integrate(Vectorize(f), minobs, maxu, h)$value return (delta) } 

But now delta(data,0.1) gives

 delta(data,0.1) [1] 0. 

That makes no sense to me. Same function, same data set, but now with the wrong value. What am I doing wrong?

Any help would be greatly appreciated.

EDIT: After taking a closer look at the Vectorize function and integrating the function, I now edited the delta function:

 delta<- function(x,h,maxu= max(x)){ minobs <- min(x) delta <- integrate(Vectorize(f, vectorize.args= c("m","h")), minobs, maxu, h)$value return (delta) } 

but now it just leads to another error:

Integration error (Vectorize (f, vectorize.args = c ("m", "h")), lower = minobs: function evaluation gave the result of the wrong length

I thought Vectorize should have prevented such errors?

Answer 1

The main problem here is that integrate expects you to have a variable that you integrate as the first argument. In the first set of code, you integrate over m . In the second set, you are trying to integrate more than x .

The shortest edit is to make a helper function to place the arguments in the required order for integrate :

 delta<- function(x,h,maxu= max(x)){ minobs <- min(x) g <- function(m) f(x,m,h) return( integrate(Vectorize(g), minobs, maxu)$value ) } 

Now you get the desired results.

 delta(data,0.1) # [1] 0.6300001 

I believe that the source of your second error was an attempt to vectorize over h , while you really only wanted to vectorize more than m . The helper function approach above fixes this problem, and also exposes the variable you want to integrate.

Note that I cannot say what you are actually trying to do here, but I also suggest this correspondence, which should be equivalent to your implementation, but it may be a little easier to follow:

 FG <- function(m, x, h) { n <- length(x) d <- function(t) pnorm((tx)/h) if(m < x[1]) return(0) if(m > x[n]) return(1) return( sum(d(m)-d(x[1]))/sum(d(x[n])-d(x[1])) ) } f<- function(m, x, h){ n <- length(x) mapply(function(m) FG(m,x,h)^n, m) } delta<- function(x, h, lb=x[1], ub=x[length(x)]) { return( integrate(f, lb, ub, x, h)$value ) }