估计均匀标记泊松过程中标记分布的分布
Estimating the distribution of marks of a homogeneous marked Poisson process
AI总结：
本文提出了一种估计均匀泊松过程中不同事件类型分布的估计器，推导了最大似然估计的强一致性和渐近正态性，并讨论了其在欧洲散裂中子源新型探测器中子检测的应用。
摘要：
本文提出了一种估计均匀泊松过程中不同事件类型分布的估计器。我们给出了分布最大似然估计器的显式解，并推导了其强一致性和渐近正态性。我们还提供了分布的顺序受限估计器，并推导了其一致性和渐近分布。推断问题导致了 Sylvester-Ramanujan 方程组。我们讨论了该估计器在欧洲散裂中子源在瑞典 Lund 开发的新型探测器中检测中子的应用。
英文摘要：
In this paper we propose an estimator of the distribution of events of different kinds in a homogeneous Poisson process. We give an explicit solution for the maximum likelihood estimator of the distribution and derive its strong consistency and asymptotic normality. We also provide an order restricted estimator of the distribution and derive its consistency and asymptotic distribution. The inference problem gives rise to a Sylvester-Ramanujan system of equations. We discuss application of the estimator to the detection of neutrons in a novel detector developed at the European Spallation Source in Lund, Sweden.
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