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.

翻译：本文提出了一种齐次泊松过程中不同类型事件分布的估计方法。我们给出了该分布的最大似然估计的显式解，并证明了其强相合性与渐近正态性。同时，我们提供了一种序约束估计方法，并推导了其相合性与渐近分布。该推断问题引出了一种西尔维斯特-拉马努金型方程组。最后，我们讨论了该估计方法在瑞典隆德欧洲散裂源研发的新型探测器中对中子检测的应用。