Loop in a dataset simulation - r

Question

I hope to get help on the following problem in R.
I have the folowing code to generate 30 column dataset based on an exponential distribuition:
x0=0
xmax=8000
xout=3000
lambda=0.0002
n=1
x1=x0+rexp(n,lambda)-xout
x2=x1+rexp(n,lambda)-xout
x3=x2+rexp(n,lambda)-xout
x4=x3+rexp(n,lambda)-xout
x5=x4+rexp(n,lambda)-xout
x6=x5+rexp(n,lambda)-xout
x7=x6+rexp(n,lambda)-xout
x8=x7+rexp(n,lambda)-xout
x9=x8+rexp(n,lambda)-xout
x10=x9+rexp(n,lambda)-xout
x11=x10+rexp(n,lambda)-xout
x12=x11+rexp(n,lambda)-xout
x13=x12+rexp(n,lambda)-xout
x14=x13+rexp(n,lambda)-xout
x15=x14+rexp(n,lambda)-xout
x16=x15+rexp(n,lambda)-xout
x17=x16+rexp(n,lambda)-xout
x18=x17+rexp(n,lambda)-xout
x19=x18+rexp(n,lambda)-xout
x20=x19+rexp(n,lambda)-xout
x21=x20+rexp(n,lambda)-xout
x22=x21+rexp(n,lambda)-xout
x23=x22+rexp(n,lambda)-xout
x24=x23+rexp(n,lambda)-xout
x25=x24+rexp(n,lambda)-xout
x26=x25+rexp(n,lambda)-xout
x27=x26+rexp(n,lambda)-xout
x28=x27+rexp(n,lambda)-xout
x29=x28+rexp(n,lambda)-xout
x30=x29+rexp(n,lambda)-xout
I have three doubts:
1 - Is there any way to write this function in a reduced form?
2 - This row (30 columns) needs to be simulated 10,000 times. How to do this in a loop?
3 - The values ​​of each cell (x1, x2, x3 ...) must be limited to the interval x0 and xmax (0-8000). How to do this?

Answer 1

That depends on what you want to do with values over 8000. Here's a solution that just takes those values and wraps them around with a modulo operator.
library(tidyverse)
test <- data.frame(x0 = rep(0, n))
for (i in 1:30) {
new_col <- sym(paste0("x", i))
old_col <- sym(paste0("x", i - 1))
test <- test %>%
mutate(!!new_col := (!!old_col + rexp(n, lambda) - xout) %% xmax)
}
I don't know how familiar you may or may not be with the tidyverse and tidy evaluation, which I've used here liberally. The !! operator, combined with sym(), turns the variable names into actual variables. The %>% operator "pipes" data from one function to the next. The := operator is needed only if you want to make assignments with a !! on the lefthand side.
I think this is my first time actually trying to post an answer on StackOverflow, so be easy on me! :)

Answer 2

As I'm fairly new to R myself, I thought it would be good practice to try to write this out. Perhaps not the most efficient code, but it works:
xmax <- 8000
xout <- 3000
lambda <- 0.0002
n <- 1
iterations <- 30
df <- data.frame(matrix(ncol = 31, nrow = iterations))
names(df) <- c(paste("x", 0:30, sep=""))
for (j in 1:iterations) {
df$x0[j] <- 0
df$x1[j] <- df$x0[j] + rexp(n,lambda)-xout
if (df$x1[j] < 0) {
df$x1[j] <- 0
}
if (df$x1[j] > 8000) {
df$x1[j] <- 8000
}
for (i in 3:31) {
df[j,i] <- df[j, i-1] + rexp(n,lambda)-xout
if (df[j,i] < 0) {
df[j,i] <- 0
}
if (df[j,i] > 8000) {
df[j,i] <- 8000
}
}
}
You can change iterations to 30000, for testing purposes I've used 30. Also I didn't know if you wanted to limit to 0 and 8000 before or after the next iterations, I've done it before.

Answer 3

Is there any way to write this function in a reduced form?
I would do it like this. Pretty sure this is equivalent.
ncol = 30
row = rexp(ncol, lambda)
row = cumsum(row) - xout * (1:ncol)
This row (30 columns) needs to be simulated 10,000 times. How to do this in a loop?
Use replicate with the code above:
sim_data = t(replicate(10000, {
row = rexp(ncol, lambda)
row = cumsum(row) - xout * (1:ncol)
}))
replicate gives 10000 columns and 30 rows. We use t() to transpose it to 10000 rows with 30 columns.
The values ​​of each cell (x1, x2, x3 ...) must be limited to the interval x0 and xmax (0-8000). How to do this?
Use pmin() and pmax(). Not sure if you want this done before or after the cumulative summing...
sim_data = t(replicate(10000, {
row = rexp(ncol, lambda)
row = cumsum(row) - xout * (1:ncol)
row = pmax(0, row)
row = pmin(xmax, row)
row
}))