Asymptotic properties of the maximum‐likelihood estimator for a class of birth‐and‐death processes admitting a unique stationary distribution

The asymptotic properties of the maximum-likelihood estimator of the parameter vector for a class of birth-and-death processes admitting a unique stationary distribution are studied. Also, it is shown that identifiability of the parameter vector with respect to the likelihood implies that the Fisher information matrix is of full rank. Two special cases of biological interest are presented. One of these, the exponential birth-and-death process, is proposed as a more appropriate model of density dependence than the logistic process.