Integration problem in R when I use the function "integrate" - r

Question

I'm trying to compute a kind of Gini index using a generated dataset.
But, I got a problem in the last integrate function.
If I try to integrate the function named f1,
R says
Error in integrate(Q, 0, p) : length(upper) == 1 is not TRUE
My code is
# set up parameters b>a>1 and the number of observations n
n <- 1000
a <- 2
b <- 4
# generate x and y
# where x follows beta distribution
# y = 10x+3
x <- rbeta(n,a,b)
y <- 10*x+3
# the starting point of the integration having problem
Q <- function(q) {
quantile(y,q)
}
# integrate the function Q from 0 to p
G <- function(p) {
integrate(Q,0,p)
}
# compute a function
L <- function(p) {
numer <- G(p)$value
dino <- G(1)$value
numer/dino
}
# the part having problem
d <- 3
f1 <- function(p) {
((1-p)^(d-2))*L(p)
}
integrate(f1,0,1) # In this integration, the aforementioned error appears
I think, the repeated integrate could make a problem but I have no idea what is the exact problem.
Please help me!

Answer 1

As mentioned by #John Coleman, integrate needs to have a vectorized function and a proper subdivisions option to fulfill the integral task. Even if you have already provided a vectorized function for integral, it is sometimes tricky to properly set the subdivisions in integrate(...,subdivisions = ).
To address your problem, I recommend integral from package pracma, where you still a vectorized function for integral (see what I have done to functions G and L), but no need to set subdivisions manually, i.e.,
library(pracma)
# set up parameters b>a>1 and the number of observations n
n <- 1000
a <- 2
b <- 4
# generate x and y
# where x follows beta distribution
# y = 10x+3
x <- rbeta(n,a,b)
y <- 10*x+3
# the starting point of the integration having problem
Q <- function(q) {
quantile(y,q)
}
# integrate the function Q from 0 to p
G <- function(p) {
integral(Q,0,p)
}
# compute a function
L <- function(p) {
numer <- Vectorize(G)(p)
dino <- G(1)
numer/dino
}
# the part having problem
d <- 3
f1 <- function(p) {
((1-p)^(d-2))*L(p)
}
res <- integral(f1,0,1)
then you will get
> res
[1] 0.1283569

Answer 2

The error that you reported is due to the fact that the function in integrate must be vectorized and integrate itself isn't vectorized.
From the help (?integrate):
f must accept a vector of inputs and produce a vector of function
evaluations at those points. The Vectorize function may be helpful to
convert f to this form.
Thus one "fix" is to replace your definition of f1 by:
f1 <- Vectorize(function(p) {
((1-p)^(d-2))*L(p)
})
But when I run the resulting code I always get:
Error in integrate(Q, 0, p) : maximum number of subdivisions reached
A solution might be to assemble a large number of quantiles and then smooth it out and use that rather than your Q, although the error here strikes me as odd.