A Unified Framework for Density Estimation under Right-Censored Point-Centred Quarter Sampling

Abstract

While the point-centred quarter method (PCQM) is widely used for density estimation, existing methods for handling right-censored data from truncated search radii rely primarily on a Poisson model assuming complete spatial randomness (CSR), leaving a critical gap for spatially aggregated populations. To address this limitation, we develop a unified likelihood- and moment-based framework for right-censored point-centred quarter sampling under both Poisson and negative binomial distribution (NBD) models. In particular, the proposed NBD-based estimators explicitly account for spatial aggregation and censoring simultaneously, extending distance-based inference beyond the CSR setting. Extensive simulations and applications to fully mapped forest plots reveal that the NBD-based MLE delivers the most robust overall performance across diverse ecological scenarios. Across more than 100 species from fully mapped forest plots, the proposed NBD-based MLE approximately reduced absolute relative bias by a median of 0.10 compared with existing censored estimators, representing a relative improvement of over 30%. Ultimately, our framework provides a rigorously validated and practically useful toolkit for analysing censored point-to-tree distance data.