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

Author

Listed:
  • P. A. W. Lewis

    (Naval Postgraduate School, Monterey, California)

  • G. S. Shedler

    (IBM Research Laboratory, San Jose, California)

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.

Suggested Citation

  • P. A. W. Lewis & G. S. Shedler, 1979. "Simulation of Nonhomogeneous Poisson Processes with Degree-Two Exponential Polynomial Rate Function," Operations Research, INFORMS, vol. 27(5), pages 1026-1040, October.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:5:p:1026-1040
    DOI: 10.1287/opre.27.5.1026
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    Cited by:

    1. Sobin Joseph & Shashi Jain, 2023. "A neural network based model for multi-dimensional nonlinear Hawkes processes," Papers 2303.03073, arXiv.org.
    2. M Hassan Tanveer & Xiaowei Wu & Antony Thomas & Chen Ming & Rolf Müller & Pratap Tokekar & Hongxiao Zhu, 2020. "A simulation framework for bio-inspired sonar sensing with Unmanned Aerial Vehicles," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-17, November.
    3. Abhinav Garg & Naman Shukla & Lavanya Marla & Sriram Somanchi, 2021. "Distribution Shift in Airline Customer Behavior during COVID-19," Papers 2111.14938, arXiv.org, revised Dec 2021.

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