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Topic: Markov transition probabilities and negative binomial distribution.
Replies: 0

 David B. Chorlian Posts: 173 Registered: 12/7/04
Markov transition probabilities and negative binomial distribution.
Posted: Mar 5, 2013 10:29 AM

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.