Trying to replicate rgeom() funtion - r

Question

As an exercise, I'm trying to write a function which replicates the rgeom() function. I want it to have the same arguments and return values. I've started out by using runif to generate a vector with x elements, but I'm not sure how to apply the probability distribution:
rgeometric <- function(x, prob) {
outcomes <- runif(x)
P <- (1 - prob)^length(x) * prob
return (P)
}
Would it be something like the following? How can I check that the distribution is geometric?
set.seed(0)
rgeometric <- function(x, prob) {
outcomes <- runif(x)
P <- (1 - prob)^length(x) * prob
for (i in x) {
x[i] <- x[i]*P
}
return (outcomes)
}
rgeometric(5, 0.4)

Answer 1

We can accomplish this task using Inverse Transform Sampling.
First, let's clear up some of your notation.
In the rgeom() function, we'll want that first argument to be n, an integer vector of length one giving the number of samples to generate:
rgeometric <- function(n, prob) {
u <- runif(n)
## do stuff
}
So how does inverse transform sampling work?
First we generate a vector u of standard uniform deviates, as shown above.
Then, for each element ui of u, we find the value of the inverse of the cumulative density function at ui.
For the geometric distribution, the CDF is 1 - (1 - prob)^(x+1); the inverse of the CDF is ceiling(log(1-u) / log(1-prob)) - 1 (link to derivation, p. 11).
So, we can complete the function like so:
rgeometric <- function(n, prob) {
u <- runif(n)
return(ceiling(log(1-u) / log(1-prob)) - 1)
}
Your last question is how can we test if the resulting samples are distributed geometric?
I don't know of a formal test that will help, but we can see it appears to work when we compare the density of 1 million random draws from this custom function to the density of 1 million random draws from base R's rgeom() function:
n <- 1e6
p <- 0.25
set.seed(0)
x <- rgeometric(n, p)
y <- rgeom(n, p)
png("so-answer.png", width = 960)
opar <- par(mfrow = c(1, 2))
plot(density(x), main = "Draws from custom function")
plot(density(y), main = "Draws from base R function")
par(opar)
dev.off()

Answer 2

Note that for the definition of the geometric function implemented by r, the random variable is the number of failures until the first success. Therefore you could do:
my_rgeom <- function(n, p){
fun <- function(p){
n <- 0
stopifnot(p>0)
while(runif(1)>p) n <- n+1
n
}
replicate(n, fun(p))
}
Now test the function:
n <- 100000
p <- 0.25
X <- rgeom(n, p)
Y <- my_rgeom(n, p)
You can do a ks.test on X and Y, though this is for continuous variables. The best thing to do is the chisq.test to determine whether the two are similar.
Lastly we could use graphical methods. eg superimposed histogram:
barplot(table(X), col = rgb(0.5, 1, 0.5, 0.4))
barplot(table(Y), add = TRUE, col = rgb(1, 0.5, 0, 0.3))
From the image above you can see that the two are nearly identical