# A truncation model for estimating Species Richness

## TL;DR

This paper introduces a semiparametric truncation model for estimating species richness, incorporating an unknown threshold to distinguish rare from abundant counts, and demonstrates its efficiency and relation to existing estimators.

## Contribution

It proposes a novel semiparametric truncation model with an unknown threshold for species richness estimation, including new estimators with proven asymptotic efficiency.

## Key findings

- The proposed estimators are asymptotically efficient.
- The model recovers Chao's lower bound estimator as a special case.
- Simulation results show competitive performance compared to existing methods.

## Abstract

We propose a truncation model for abundance distribution in the species richness estimation. This model is inherently semiparametric and incorporates an unknown truncation threshold between rare and abundant counts observations. Using the conditional likelihood, we derive a class of estimators for the parameters in the model by a stepwise maximisation. The species richness estimator is given by the integer maximising the binomial likelihood when all other parameters in the model are know. Under regularity conditions, we show that the estimators of the model parameters are asymptotically efficient. We recover the Chao$^{'}$s lower bound estimator of species richeness when the model is a unicomponent Poisson$^{'}$s model. So, it is an element of our class of estimators. In a simulation study, we show the performances of the proposed method and compare it to some others.