The Estimation of the Parameters of a Birth and Death Process
P. A. P. Moran · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1953
Summary In a previous paper the estimation of the sum λ + μ of the parameters of a simple birth and death process was considered. In the present paper we consider the estimation of λ(λ + μ)−1. This problem is equivalent to the problem of estimating the probabilities of steps to the right and left from an observed realization of a random walk which has one absorbing boundary and which is terminated, if necessary, after a preassigned number of steps. The properties of various estimators are considered.