A continuous piecewise-linear NHPP intensity function estimator

David Malcolm Nicol, Lawrence M. Leemis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the problem of using either grouped observations of a counting process over a period or prescribed constant mean counts to create an intensity function for a Non-Homogeneous Poisson Process (NHPP) that estimates the observed process, and satisfies several constraints. First, we require that the estimator's mean value over an observation interval be equal to the mean number of observations in that interval; second, we require that the intensity function be continuous; third, we require that the function be piecewise linear. Optionally, we may also require that the intensity value at the end of the period be identical to the intensity value at the beginning of the period, for application in contexts in which the period of interest is inherently cyclic, e.g., a day, or a week. An objective of the estimator is that it should be 'smooth,' which will be defined subsequently. Our approach is to define a class of continuous piecewise-linear intensity functions and formulate the problem as a constrained quadratic programming problem, approachable through the solution of a simultaneous set of linear equations. We describe the method, identify conditions under which feasible solutions are assured to exist, and study the behavior of the solutions on an example problem.

Original languageEnglish (US)
Title of host publicationProceedings of the 2014 Winter Simulation Conference, WSC 2014
EditorsAndreas Tolk, Levent Yilmaz, Saikou Y. Diallo, Ilya O. Ryzhov
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages498-509
Number of pages12
ISBN (Electronic)9781479974863
DOIs
StatePublished - Jan 23 2015
Event2014 Winter Simulation Conference, WSC 2014 - Savannah, United States
Duration: Dec 7 2014Dec 10 2014

Publication series

NameProceedings - Winter Simulation Conference
Volume2015-January
ISSN (Print)0891-7736

Other

Other2014 Winter Simulation Conference, WSC 2014
CountryUnited States
CitySavannah
Period12/7/1412/10/14

Fingerprint

Non-homogeneous Poisson Process
Intensity Function
Piecewise Linear
Estimator
Counting Process
Interval
Quadratic programming
Linear equations
Quadratic Programming
Mean Value
Linear Function
Linear equation
Count
Estimate
Observation

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Computer Science Applications

Cite this

Nicol, D. M., & Leemis, L. M. (2015). A continuous piecewise-linear NHPP intensity function estimator. In A. Tolk, L. Yilmaz, S. Y. Diallo, & I. O. Ryzhov (Eds.), Proceedings of the 2014 Winter Simulation Conference, WSC 2014 (pp. 498-509). [7019915] (Proceedings - Winter Simulation Conference; Vol. 2015-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/WSC.2014.7019915

A continuous piecewise-linear NHPP intensity function estimator. / Nicol, David Malcolm; Leemis, Lawrence M.

Proceedings of the 2014 Winter Simulation Conference, WSC 2014. ed. / Andreas Tolk; Levent Yilmaz; Saikou Y. Diallo; Ilya O. Ryzhov. Institute of Electrical and Electronics Engineers Inc., 2015. p. 498-509 7019915 (Proceedings - Winter Simulation Conference; Vol. 2015-January).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nicol, DM & Leemis, LM 2015, A continuous piecewise-linear NHPP intensity function estimator. in A Tolk, L Yilmaz, SY Diallo & IO Ryzhov (eds), Proceedings of the 2014 Winter Simulation Conference, WSC 2014., 7019915, Proceedings - Winter Simulation Conference, vol. 2015-January, Institute of Electrical and Electronics Engineers Inc., pp. 498-509, 2014 Winter Simulation Conference, WSC 2014, Savannah, United States, 12/7/14. https://doi.org/10.1109/WSC.2014.7019915
Nicol DM, Leemis LM. A continuous piecewise-linear NHPP intensity function estimator. In Tolk A, Yilmaz L, Diallo SY, Ryzhov IO, editors, Proceedings of the 2014 Winter Simulation Conference, WSC 2014. Institute of Electrical and Electronics Engineers Inc. 2015. p. 498-509. 7019915. (Proceedings - Winter Simulation Conference). https://doi.org/10.1109/WSC.2014.7019915
Nicol, David Malcolm ; Leemis, Lawrence M. / A continuous piecewise-linear NHPP intensity function estimator. Proceedings of the 2014 Winter Simulation Conference, WSC 2014. editor / Andreas Tolk ; Levent Yilmaz ; Saikou Y. Diallo ; Ilya O. Ryzhov. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 498-509 (Proceedings - Winter Simulation Conference).
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