function to simulate proportional sum of exponential variables

sumExp.R

# function to simulate proportional sum of exponential variables
# p = p1,p2,p3,...,pn sum to one
# r = rates for exponential random variables
sumExp <- function(p,r){
  if(sum(p) != 1) stop("p does not sum to 1")
  if(length(p) != length(r)) stop("p and r not equal lengths")
  x <- rexp(length(r),rate = r)
  crossprod(p,x)
}

# Example 
out <- replicate(n = 10000, expr = sumExp(p=c(0.1,0.2,0.3,0.4), r=c(0.5,1,1.5,3)))
hist(out, freq = F)
lines(density(out))