Estimating parameters of continuous-time linear birth-death-immigration
processes, observed discretely at unevenly spaced time points, is a recurring
theme in statistical analyses of population dynamics. Viewing this task as a
missing data problem, we develop two novel expectation-maximization (EM)
algorithms. When the rate of immigration is either zero or proportional to the
birth rate, we use Kendall's generating function method to reduce the E-step of
the EM algorithm, as well as calculation of the Fisher information, to one
dimensional integration.