I have looked for an answer for a while, but with no luck. I am trying to develop a discrete time Markov model. Presently, I have 5 states, with the 5th state being the absorbing state. I also know the variable time durations that each state stays in. So say state one might take 20 years to transition to state 2 and this is normally distributed. Is there a way to calculate the transition matrix with this data?
update: I'm thinking along the lines of Monte-carlo Markov chain simulation, but I'm unsure how to structure the MCMC model.