A Truncation Model for Estimating Species Richness

We propose a truncation model for the abundance distribution in species richness estimation. This model is inherently semiparametric and incorporates an unknown truncation threshold between rare and abundant observations. Using the conditional likelihood, we derive a class of estimators for the parameters in this model by stepwise maximization. The species richness estimator is given by the integer maximizing the binomial likelihood, given all other parameters in the model. Under regularity conditions, we show that our estimators of the model parameters are asymptotically efficient. We recover Chaos lower bound estimator of species richness when the parametric part of the model is single-component Poisson. Thus our class of estimators strictly generalized the latter. We illustrate the performance of the proposed method in a simulation study, and compare it favorably to other widely-used estimators. We also give an application to estimating the number of distinct vocabulary words in French playwright Molière's Tartuffe.