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

M. Mandjes, L. Ravner

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)41-73
Number of pages33
JournalStochastic Processes and their Applications
Volume133
DOIs
StatePublished - Mar 2021
Externally publishedYes

Bibliographical note

Funding Information:
Both authors? research is partly funded by NWO Gravitation project NETWORKS (The Netherlands), grant number 024.002.003.

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

  • Convergence to stationarity
  • Hypothesis testing
  • Lévy-driven storage system
  • Poisson sampling

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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