Modeling duration in a hidden Markov model with the exponential family

A procedure for modeling duration with some PDF (probability density function) or PMF (probability mass function) in the exponential family is presented. A means of selecting an appropriate member of the exponential family is suggested. The parameter estimation procedure presented here offers several advantages over other methods of duration modeling. First, the duration PMF can be found directly, rather than sampling and truncating the optimum density. Secondly, the optimum duration parameters are found from Ferguson´s nonparametric PMF. This simplifies reestimation because the operation of casting a nonparametric PMF to the desired parametric family can be completely separated from the forward and backward algorithms. Thirdly, several competing members of the exponential family can be evaluated quickly for each state in the HMM. This makes it possible to model each state´s duration with the best member from a set of parametric PMFs in the exponential family. Finally, the solution holds for an PDF or PMF in the exponential family, which includes a large number of promising candidates.<>