Simulation methods for Poisson processes in nonstationary systems
Abstract
The nonhomogeneous Poisson process is a widely used model for a series of events (stochastic point process) in which the rate or intensity of occurrence of points varies, usually with time. The process has the characteristic properties that the number of points in any finite set of nonoverlapping intervals are mutually independent random varialbes, and that the number of points in any of these intervals has a Poisson distribution. This paper first discusses several general methods for simulation of the one-dimensional nonhomogeneous Poisson process. Then a particular and very efficient method for simulation of nonhomogeneous Poisson processes is stated with log-linear rate function. The method is based on an identity relating the nonhomogeneous Poisson process to the gap statistics from a random number of exponential random variables with suitably chosen parameters. Finally, a simple and relatively efficient new method for simulation of one-dimensional and two-dimensional nonhomogeneous Poisson processes is described. The method is applicable for any given rate function and is based on controlled deletion of points in a Poisson process with a rate function that dominates the given rate function
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.NPS Report Number
NPS55-78-019Related items
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Simulation of Nonhomogeneous Poisson Processes by Thinning
Lewis, P.A.W.; Shedler, G.S. (Monterey, California. Naval Postgraduate School, 1978-06); NPS-55-78-014A simple and relatively efficient method for simulating one-dimensional and two-dimensional nonhomogeneous Poisson processes is presented. The method is applicable for any rate function and is based on controlled deletion ... -
Simulation of Nonhomogeneous Poisson Processes by Thinning
Lewis, P.A.W.; Shedler, G.S. (1979);A simple and relatively efficient method for simulating one‐dimensional and two‐dimensional nonhomogeneous Poisson processes is presented The method is applicable for any rate function and is based on controlled deletion ... -
Simulation Methods for Poisson Processes in Nonstationary Systems
Lewis, Peter A.W.; Shedler, Gerald S. (1978);The nonhomogeneous Poisson process is a widely used model for a series of events (stochastic point process) in which the "rate" or "intensity" of occurrence of points varies, usually with time. The process has the ...