A realization of a Markov process generates a sequence of interval lengths between transition from one state to another. A natural way of modeling the distribution of the lengths is as a negative binomial distribution. Is there any relatively easy way to estimate the two parameters characterizing the negative binomial distribution from the n * (n - 1) parameters characterizing the Markov process? I am particularly interested in small values of n. I have data from which I can estimate these parameters, but I suspect that the process is not well modeled as a simple Markov process. I would appreciate references to any articles discussing this topic and suggesting different modeling approaches.