Simulation of Nonhomogeneous Poisson Processes with Degree-Two Exponential Polynomial Rate Function

P. A. W. Lewis and G. S. Shedler
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P. A. W. Lewis: Naval Postgraduate School, Monterey, California
G. S. Shedler: IBM Research Laboratory, San Jose, California

Operations Research, 1979, vol. 27, issue 5, 1026-1040

Abstract: A new method for simulating a nonhomogeneous Poisson process with rate function λ( t ) = exp{α 0 + α 1 t + a 2 t 2 } in a fixed time interval (0, t 0 ] is given. The method is based on a decomposition of the process, it employs a rejection technique, in conjunction with a method for simulating the nonhomogeneous Poisson process with rate function exp {γ 0 + γ 1 t } by generation of gap statistics from a random number of exponential random variables with suitably chosen parameters. The proposed method for the degree-two exponential polynomial model is more efficient than time-scale transformation of a homogeneous Poisson process, and should be applicable to other rate function models.

Date: 1979
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