An exponential hidden Markov model (EHMM) is a hidden Markov model which consists of a pair of stochastic processes
is influenced by
, which is assumed to form a Markov chain.
is not observed.
is an observation process and given has exponential distribution. In this paper, we estimate the parameter of EHMM and study the convergence of the parameter estimator sequence. EHMM is characterized by a parameter
where is a transition matrix of and is a vector of parameters of probability density function of given . To determine the parameter estimator, a maximum likelihood method is used. Numerical approximation is used through an Expectation Maximization (EM) algorithm. Under the continuous assumption, the sequence
obtained by the EM algorithm, converges to which is the stationary point of ln and the sequence
increasingly converges to ln .