Computing an NPMLE for a mixing distribution in two closed heterogeneous population size models.

Binomial and geometric mixtures can be used to model data gathered in capture-recapture surveys of animal populations, removal surveys of harvest populations, registrations of disease populations, ecological species census, and so on. To compute a nonparametric maximum likelihood estimator for the mixing distribution of heterogeneous capture probabilities, we consider a conditional approach and use a reliable and fast integrative procedure which combines the EM algorithm to increase the likelihood and the vertex-exchange method to update the number of support points. A convergent Newtonian algorithm is used in the M-step of the EM algorithm.