According to the following - https://dylanspicker.com/courses/STAT437/content/041%20+%20044.%20Lecture%20Notes.pdf the PH and AFT models are equivalent for Weibull distribution.
Does this implies the event-time should be distributed similarly? The following code seems to contradict it. What am I missing?
n <- 100000
rho <- 2 # scale of h_0 that follow weibull (lambda)
k <- 3 # shape of h_0 that follows weibull (v)
x <- rnorm(n)
## AFT
t_aft <- exp(log(rho) + x + 1 / k * rweibull(n, scale=rho, shape=k))
## PH
# sampling is done based on bender 2003
t_ph <- (1 / rho) * (-log(runif(n)) * exp(k * x))^(1 / k)
plot(density(t_ph))
lines(density(t_aft), col = 'red')
