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.

翻译：虽然点中心象限法（PCQM）广泛应用于密度估计，但现有处理截断搜索半径下右删失数据的方法主要依赖于假设完全空间随机性（CSR）的泊松模型，这导致在空间聚集种群分析中存在关键空白。为弥补这一局限，我们发展了一个基于似然与矩的统一框架，用于处理泊松模型和负二项分布（NBD）模型下的右删失点中心象限抽样。特别地，所提出的基于NBD的估计量能同步显式处理空间聚集与删失效应，将距离推断拓展至CSR假设之外。通过大规模模拟及完全测绘森林样地数据的应用表明，基于NBD的最大似然估计（MLE）在不同生态场景下展现出最稳健的整体性能。针对来自完全测绘森林样地的100余个物种，与现有删失估计量相比，所提出的基于NBD的MLE将绝对相对偏差中位数降低了约0.10，相对改进幅度超过30%。最终，我们的框架为分析删失点-树距离数据提供了经严格验证且具有实践应用价值的工具包。