摘要
The estimation of abundance from presence-absence data is an intriguing problem in applied statistics. The classical Poisson model makes strong independence and homogeneity assumptions and in practice generally underestimates the true abundance. A controversial ad hoc method based on negative-binomial counts (Am. Nat.) has been empirically successful but lacks theoretical justification. We first present an alternative estimator of abundance based on a paired negative binomial model that is consistent and asymptotically normally distributed. A quadruple negative binomial extension is also developed, which yields the previous ad hoc approach and resolves the controversy in the literature. We examine the performance of the estimators in a simulation study and estimate the abundance of 44 tree species in a permanent forest plot.