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Nonparametric Estimation of the Cumulative Intensity Function for a Nonhomogeneous Poisson Process

Author

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  • Lawrence M. Leemis

    (The University of Oklahoma, School of Industrial Engineering, 202 West Boyd, Room 124, Norman, Oklahoma 73019)

Abstract

A nonparametric technique for estimating the cumulative intensity function of a nonhomogeneous Poisson process from one or more realizations is developed. This technique does not require any arbitrary parameters from the modeler, and the estimated cumulative intensity function can be used to generate a point process for Monte Carlo simulation by inversion. Three examples are given.

Suggested Citation

  • Lawrence M. Leemis, 1991. "Nonparametric Estimation of the Cumulative Intensity Function for a Nonhomogeneous Poisson Process," Management Science, INFORMS, vol. 37(7), pages 886-900, July.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:7:p:886-900
    DOI: 10.1287/mnsc.37.7.886
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    Cited by:

    1. Alexopoulos, Christos & Goldsman, David & Fontanesi, John & Kopald, David & Wilson, James R., 2008. "Modeling patient arrivals in community clinics," Omega, Elsevier, vol. 36(1), pages 33-43, February.
    2. Xinan Yang & Arne K. Strauss & Christine S. M. Currie & Richard Eglese, 2016. "Choice-Based Demand Management and Vehicle Routing in E-Fulfillment," Transportation Science, INFORMS, vol. 50(2), pages 473-488, May.
    3. Bradford L. Arkin & Lawrence M. Leemis, 2000. "Nonparametric Estimation of the Cumulative Intensity Function for a Nonhomogeneous Poisson Process from Overlapping Realizations," Management Science, INFORMS, vol. 46(7), pages 989-998, July.
    4. Huifen Chen & Bruce Schmeiser, 2013. "I-SMOOTH: Iteratively Smoothing Mean-Constrained and Nonnegative Piecewise-Constant Functions," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 432-445, August.
    5. Ma, Ni & Whitt, Ward, 2016. "Efficient simulation of non-Poisson non-stationary point processes to study queueing approximations," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 202-207.
    6. Hainan Guo & David Goldsman & Kwok-Leung Tsui & Yu Zhou & Shui-Yee Wong, 2016. "Using simulation and optimisation to characterise durations of emergency department service times with incomplete data," International Journal of Production Research, Taylor & Francis Journals, vol. 54(21), pages 6494-6511, November.
    7. Yang, Feng & Liu, Jingang, 2012. "Simulation-based transfer function modeling for transient analysis of general queueing systems," European Journal of Operational Research, Elsevier, vol. 223(1), pages 150-166.
    8. Paola Cappanera & Filippo Visintin & Carlo Banditori & Daniele Feo, 2019. "Evaluating the long-term effects of appointment scheduling policies in a magnetic resonance imaging setting," Flexible Services and Manufacturing Journal, Springer, vol. 31(1), pages 212-254, March.
    9. Michael E. Kuhl & Sachin G. Sumant & James R. Wilson, 2006. "An Automated Multiresolution Procedure for Modeling Complex Arrival Processes," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 3-18, February.
    10. Yong-Hong Kuo & Omar Rado & Benedetta Lupia & Janny M. Y. Leung & Colin A. Graham, 2016. "Improving the efficiency of a hospital emergency department: a simulation study with indirectly imputed service-time distributions," Flexible Services and Manufacturing Journal, Springer, vol. 28(1), pages 120-147, June.
    11. Cuffe, Barry P. & Friedman, Moshe F., 1996. "The joint distribution of the number of occurrences of two interrelated Poisson processes," European Journal of Operational Research, Elsevier, vol. 89(3), pages 660-667, March.
    12. Ira Gerhardt & Barry L. Nelson, 2009. "Transforming Renewal Processes for Simulation of Nonstationary Arrival Processes," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 630-640, November.
    13. M. Arns & P. Buchholz & A. Panchenko, 2010. "On the Numerical Analysis of Inhomogeneous Continuous-Time Markov Chains," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 416-432, August.

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