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Hypothesis testing for a Lévy-driven storage system by Poisson sampling

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  • Mandjes, M.
  • Ravner, L.

Abstract

This paper focuses on hypothesis testing for the input of a Lévy-driven storage system by sampling of the storage level. As the likelihood is not explicit we propose two tests that rely on transformation of the data. The first approach uses i.i.d. ‘quasi-busy-periods’ between observations of zero workload. The distribution of the duration of quasi-busy-periods is determined. The second method is a conditional likelihood ratio test based on the Bernoulli events of observing a zero or positive workload, conditional on the previous workload. Performance analysis is presented for both tests along with speed-of-convergence results, that are of independent interest.

Suggested Citation

  • Mandjes, M. & Ravner, L., 2021. "Hypothesis testing for a Lévy-driven storage system by Poisson sampling," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 41-73.
    • Handle: RePEc:eee:spapps:v:133:y:2021:i:c:p:41-73
    DOI: 10.1016/j.spa.2020.11.005
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    References listed on IDEAS

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    3. U. Narayan Bhat & S. Subba Rao, 1972. "A Statistical Technique for the Control of Traffic Intensity in the Queuing Systems M / G /1 and GI / M /1," Operations Research, INFORMS, vol. 20(5), pages 955-966, October.
    4. Peter W. Glynn & Benjamin Melamed & Ward Whitt, 1993. "Estimating Customer and Time Averages," Operations Research, INFORMS, vol. 41(2), pages 400-408, April.
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    Cited by:

    1. Liron Ravner, 2022. "Queue input estimation from discrete workload observations," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 541-543, April.

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