The non-homogeneous Poisson process (NHPP) and the renewal process (RP) are two stochastic point process models that are commonly used to describe the pattern of repeated occurrence data. An inhomogeneous Gamma process (IGP) is a point process model that generalizes both the NHPP and a particular RP, commonly referred to as a Gamma renewal process, which has interarrival times that are i.i.d. gamma random variables with unit scale parameter and shape parameter $\kappa >0$. This article focuses on a particular class of the IGP which has a periodic or almost periodic baseline intensity function and a shape parameter $\kappa \in \mathbb{N}$. This model deals with point events that show a pattern of periodicity or almost periodicity. Consistent estimators of unknown parameters are constructed mainly by the Bartlett periodogram. Simulation results that support theoretical findings are provided.

中文翻译：

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非齐次伽玛点过程数据中周期性或几乎周期性的估计

非齐次泊松过程 (NHPP) 和更新过程 (RP) 是两个随机点过程模型，通常用于描述重复出现数据的模式。非齐次伽玛过程 (IGP) 是一种点过程模型，它概括了 NHPP 和特定 RP，通常称为伽玛更新过程，其到达间隔时间是具有单位尺度参数和形状参数的 iid 伽玛随机变量$\kappa >0$. 本文重点介绍具有周期性或几乎周期性基线强度函数和形状参数的 IGP 的特定类别$\kappa \in \mathbb{N}$. 该模型处理显示周期性或几乎周期性模式的点事件。未知参数的一致估计量主要由 Bartlett 周期图构建。提供了支持理论发现的模拟结果。