The nhppp package for simulating non-homogeneous Poisson point processes in R

Area of Science:

• Computational Statistics
• Simulation Methods
• Point Process Theory

Background:

• Discrete event and statistical simulations require efficient methods for generating event times.
• Non-homogeneous Poisson point processes (NHPPPs) are fundamental models for event occurrences over time.
• Existing simulation methods for NHPPPs can be computationally intensive or memory-demanding.

Purpose of the Study:

• To introduce the nhppp R package for fast and memory-efficient simulation of one-dimensional NHPPPs.
• To provide researchers with reliable tools for sampling event times in complex simulations.
• To implement and evaluate three distinct, provably correct NHPPP simulation algorithms.

Main Methods:

• Time-transformation of a standard homogeneous Poisson process using the inverse of the integrated intensity function.
• Generation of Poisson-distributed order statistics from a specified density function.
• Thinning of a majorizing NHPPP employing an acceptance-rejection scheme.

Main Results:

• The nhppp package provides functions based on three theoretically sound algorithms for NHPPP event simulation.
• Numerical accuracy and time performance of the implemented algorithms were rigorously studied.
• The package demonstrates efficient performance with a small memory footprint.

Conclusions:

• The nhppp R package offers a valuable, efficient, and accurate solution for simulating NHPPPs.
• It facilitates the integration of NHPPP event generation into discrete event and statistical simulations.
• The package includes reproducible examples, promoting ease of use and adoption.