Suppose you are tasked with simulating a process where the inter-arrival times are not exponentially distributed, but Gamma(2, λ) under the fixed-count scheme, say 25 events, subject to the constraint that you must use the integral transform method of the Gamma distribution.

Im working using R.

The code below is what i used for an exponential distribution:
1 R> n = 25
2 R> lambda = 10
3 R> u = runif(n,0,1)
4 R> t = -1/lambda*log(1-u)

How would you modify it for a gamma distribution simulation.

Thanks