Distance-based point-centered quarter method (PCQM) is widely used for population density estimation, yet its performance is challenged by right-censored observations arising from a truncated search radius. Existing methods for addressing such right-censored data are predominantly developed under the assumption of complete spatial randomness (CSR) using a Poisson model, while approaches for spatially aggregated populations--despite the negative binomial distribution (NBD) being well-established for uncensored distance sampling--remain lacking a systematic framework. This study presents a systematic set of censored distance-based estimators under these two core frameworks. We develop both moment-based estimators and maximum likelihood estimators (MLEs) under these two core frameworks, extending classical results to the censored setting for CSR populations and providing new inference tools for aggregated populations under the NBD model. Extensive simulations and applications to fully-censused forest plot data demonstrate that the NBD-based MLE achieves the highest accuracy and robustness across a wide range of ecological scenarios, with a median relative bias below 20\% in most empirical scenarios--a level of estimation accuracy that cannot be consistently guaranteed by other competing methods, providing a rigorously validated toolkit for analyzing censored point-to-tree distance data.

翻译：基于距离的点中心四分法（PCQM）被广泛应用于种群密度估计，但其性能受到截断搜索半径导致的右删失观测数据的挑战。现有处理此类右删失数据的方法主要基于完全空间随机性（CSR）假设下的泊松模型，而对于空间聚集种群的方法——尽管负二项分布（NBD）在未删失距离抽样中已得到充分验证——仍缺乏系统化框架。本研究在这两个核心框架下提出了一套系统的删失距离估计方法。我们分别基于矩估计法和最大似然估计法（MLE）发展了两种框架下的估计量：将经典结果扩展至CSR种群的删失场景，并为NBD模型下的聚集种群提供了新的推断工具。大量模拟实验及对全普查森林样地数据的应用表明，基于NBD的MLE在各类生态场景中均表现出最高的准确性与稳健性，在多数实证场景中相对偏差中位数低于20%——这一估计精度水平是其他竞争方法无法稳定保证的，从而为分析删失点-树距离数据提供了经过严格验证的工具集。