A comparison of two algorithms for the simulation of non-homogeneous poisson processes with degree-two exponential polynomial intensity function.

By simulating several cases of non-homogeneity Poisson processes with log-quadratic intensity functions, it is shown that the Poisson-decomposition and gap statistic algorithm substantially reduces computation time from that required by an algorithm that uses a time-scale transformation of a homogeneous Poisson process.

Abstract

Two algorithms for generating a non-homogeneous Poisson process with log-quadratic intensity function are implemented into computer programs and compared for relative speed, core storage requirements and fidelity. By simulating several cases of non-homogeneous Poisson processes with log-quadratic intensity functions it is shown that the Poisson-decomposition and gap statistic algorithm substantially reduces computation time from that required by an algorithm that uses a time-scale transformation of a homogeneous Poisson process. The experience gained from implementing the algorithm has led to several possibilities which are suggested for improving the efficiency of the Poisson-decomposition and gap statistic algorithm.